Keywords: Aerospace, Switched systems, Optimal control
Abstract: In this paper, we study the limit cycle oscillations of multiple double integrators with coupled dynamics, subject to a constant disturbance term and switching inputs. Such systems arise in a variety of control problems where the minimization of both fuel and number of input transitions is a key requirement. The problem of finding the minimum switching limit cycle, among all the fuel-optimal solutions satisfying given state constraints, is addressed. Starting from well known results available for a single double integrator, two suboptimal solutions are provided for the multivariable case. First, an analytic upper bound on the number of input switchings is derived. Then, a less conservative numerical solution exploiting the additional degrees of freedom provided by the phases of the limit cycles is presented. The proposed techniques are compared on two simulation examples.

Keywords: Switched systems, Linear systems
Abstract: This paper analyses the design of switched control of continuous-time switched systems, satisfying dwell-time constraints. These constraints are normally imposed to avoid the undesired phenomenon of chattering, which can damage physical devices used in the implementation of such systems. To this end, we define a discrete-time constrained switched system, which, together with sampled-data techniques, allows us to model this problem and design the switching rule, ensuring stability and performance to the closed-loop system. Numerical examples illustrate the developed theory.

Keywords: Switched systems, LMIs
Abstract: This paper addresses the problem of determining the input signals of switching devices, e.g. the duty cycle of electronic valves and converters, in order to drive the system state to a desired value at the equilibrium. For this purpose, the closed loop system is represented as a switched system, where the model of the subsystems are known, and a switching rule is determined in order to solve the tracking problem. The input signals of the switching devices are obtained by performing online convex combinations defined from the switching rule and some auxiliary parameters specifying the upper and lower bounds of the signals. The model of the subsystems are affine and can be obtained by usual identification methods, typically by performing experiments with the system under specific operation conditions associated with the switching devices. The switching rule is determined by solving an LMI problem where a guaranteed cost is minimized and global asymptotic stability of the tracking error dynamics is guaranteed even if sliding motions occur at any switching surface of the system. The potential of the results are illustrated on a true refrigeration system, namely a domestic refrigerator, where the purpose is to control the temperature in two compartments of the refrigerator: the fresh food and the freezer compartments. The control signals to be determined are those associated with the definition of the compressor rotation and the distribution of the refrigeration fluid to the compartments.

Keywords: Switched systems, Hybrid systems, Optimal control
Abstract: This paper addresses the problem of optimally scheduling the mode sequence and mode duration for switched dynamical systems under dwell time constraints that describe how long a system has to stay in a mode before they can switch to another mode. The schedule should minimize a given cost functional defined on the state trajectory. The topology of the optimization space for switched dynamical systems with and without dwell time constraints is investigated and it is shown that the notion of local optimality must be replaced by stationarity with regards to a suitably chosen optimality function when dwell time constraints are present. Hence, an optimality function is proposed to characterize the solution to the dwell time problem as points that satisfy optimality condition defined in terms of optimality function. A conceptual algorithm is presented to solve the mode scheduling problem and its convergence to stationary points is proved. A numerical example is given to highlight the algorithm.

Keywords: Switched systems, Stability of NL systems, Sliding mode control
Abstract: We present an approach to study contraction of sliding mode solutions in n-dimensional Filippov systems and characterize global convergence of their trajectories towards each other. The results extend to n-dimensional systems with discontinuous right-hand sides the approach proposed in [Liuzza, di Bernardo, 2013] for the planar case. Sufficient conditions for the incremental stability of the sliding vector field are derived using contraction theory. These are then complemented with conditions for global attractivity of the sliding region to prove global convergence of trajectories of the Filippov system of interest towards each other within a region of interest. The theoretical derivations are illustrated by means of a representative numerical example.

Keywords: Switched systems, Uncertain systems
Abstract: This paper presents a linear programming-based method for finding Lyapunov functions of switched systems with polynomial vector fields and parametric uncertainties. We propose to utilize a certificate of positivity in the Bernstein basis to find a Lyapunov function. A certificate of positivity in the Bernstein basis always exists if a polynomial is positive, and the Bernstein basis is shown to be well conditioned.

Keywords: H infinity control, Stability of hybrid systems, LMIs
Abstract: This paper deals with the hybrid output regulation problem for a class of linear impulsive systems with average dwell time. The hybrid regulator is constructed as a linear impulsive system that undergoes synchronous impulses with the controlled plant, and the hybrid synthesis conditions are formulated in terms of two matrix equations plus a set of linear matrix inequalities (LMIs). With the proposed hybrid synthesis scheme, both continuous-time and discrete-time dynamics of the hybrid regulator can be jointly synthesized by solving a convex optimization problem of minimizing the weighted mathcal{L}_2 gain from the perturbation signal to the error output. A numerical example is used to demonstrate the proposed approach.

Keywords: Hybrid systems, Linear systems
Abstract: In this paper, we deal with the output regulation problem for linear hybrid systems in the presence of unpredictable jumps, hence with arbitrary time domains. In particular we provide necessary and sufficient conditions for the solvability of the hybrid regulation problem, which non-trivially extend the classical conditions of regulation for LTI non-hybrid systems. Interestingly, differently from the latter, the former conditions are intrinsically nonlinear, since the dynamics of the interconnected system restricted to the error-zeroing invariant subspace may not be limited, as in the non-hybrid case, to those of the exosystem E. Then, we explore the relation between the discussed necessary and sufficient conditions and the constructive approach provided by the subspace invariant algorithm.

Keywords: Hybrid systems, Nonlinear systems, Robust control
Abstract: The paper deals with the problem of robust output regulation for minimum-phase nonlinear systems in a semiglobal setting. We present a different perspective to the problem of adaptive regulation in which prediction error identification methods, which are routinely used in other control contexts, can be adopted to design robust nonlinear regulators. The proposed control structure combines continuous-time dynamics and "hybrid identifiers", the latter specifically designed to estimate the actual steady state control law. Besides presenting the main idea and a general framework, the paper addresses the specific case in which a linear regression law is used as model structure for the steady state control law and a least square optimisation criterion is adopted as estimation method. The proposed framework encompasses existing frameworks proposed so far in the nonlinear continuous-time literature.

Keywords: Nonlinear systems, Algebraic/geometric methods, Output feedback and Observers
Abstract: This paper is about the nonlinear error feedback regulator problem. The plant is a nonlinear finite-dimensional single-input-single-output system and it is locally exponentially stable around the origin. It is driven by a linear exosystem with simple eigenvalues on the imaginary axis. The reference signal that the plant output must track is obtained from the state of the exosystem, in a nonlinear way. The regulator problem is to design a dynamic feedback controller, with the tracking error as its input and the control input to the plant as its output, such that (i) the closed-loop system of the plant and the controller is locally exponentially stable and (ii) the tracking error tends to zero for all sufficiently small initial conditions of the plant, the controller and the exosystem. Under the assumption that the regulator problem is solvable, i.e., there exists a solution to the so-called nonlinear regulator equations, we propose a nonlinear controller of order equal to that of the exosystem to solve the regulator problem. In contrast, previous results on the regulator problem have typically proposed controllers of a larger order. The motivation for the nonlinear controller designed in this work is the structure of a linear controller that solves the regulator problem for the plant linearized around the origin, when the reference and disturbance signals are linear functions of the exosystem state. The nonlinear controller has the same state and control operators as the linear controller and the linearization of its (possibly nonlinear) observation operator is the observation operator of the linear controller. An example and a counterexample illustrating the theory are presented.

Keywords: Nonlinear systems, Networked control systems, Robust control
Abstract: The conventional output regulation problem aims to achieve reference tracking and disturbance rejection while references and disturbances are generated by an autonomous exosystem. When the exosystem is perturbed by an external event, a novel robust perturbed output regulation problem is formulated and solved in this paper. The formulation arises from a kind of synchronization problem of multiple agents. Hence, the proposed solution leads to a decentralized control algorithm for synchronization of multiple agents with nonlinear heterogeneous dynamics.

Keywords: Distributed parameter systems, Robust control
Abstract: In this paper we employ a new controller structure in solving the robust output regulation problem for a linear distributed parameter system with finite or infinite-dimensional exosystems. In the case of an infinite-dimensional exosystem we also present additional conditions for achieving polynomial or logarithmic nonuniform decay rates for the closed-loop semigroup.

Keywords: Sliding mode control, Constrained control, Uncertain systems
Abstract: This paper deals with the design of a third order Sliding Mode Control (SMC) algorithm for a perturbed chain of integrators with box constraints on state variables. The proposed strategy takes into account a robust generalization of the so-called Fuller’s Problem, which is a standard optimal control problem for a chain of integrators under critical uncertainty condition, and proves to steer the system trajectories to the origin of the state space in finite time, while satisfying the imposed constraints. The proposed algorithm is tested in simulation to solve a trajectory-tracking problem for a nonholonomic car.

Keywords: Sliding mode control, Robust adaptive control, Biomedical systems
Abstract: In this article, we develop an output feedback adaptive sliding mode controller for a general multicompartment lung mechanics model with nonlinear resistance and compliance respiratory parameters. Specifically, for a given clinically plausible reference volume pattern, we develop an adaptive sliding mode controller that accounts for input pressure and rate saturation constraints to automatically adjust the applied input so that the total lung volume tracks the given reference pattern. The proposed tracking control framework is applied to a two-compartment lung mechanics model with nonlinear lung compliance and resistance parameters.

Keywords: Sliding mode control, Nonlinear systems, Robotics
Abstract: This paper presents a fast nonsingular integral terminal sliding mode control (FNITSMC) for a class of nonlinear systems. First, a novel fast nonsingular integral terminal sliding mode surface (FNITSMS) is designed by introducing power integral terms which contain a boundary-like structure. Next, by employing FNITSMS and the equivalent control technique, the FNITSMC is proposed to achieve the finite-time convergence of the system states. Compared with many existing works on terminal sliding mode control (TSMC), the proposed FNITSMC exhibits three attractive features: (i) can avoid the singularity problem without any constraint, and provide faster responses by tuning the parameters in FNITSMS; (ii) for constant or eventually constant disturbances, zero steady-state error can be achieved when a boundary layer is used to alleviate chattering; (iii) the switching gain is only required to be designed greater than the bound of the disturbance. Finally, Simulation results of both the numerical and application examples show the effectiveness of the proposed control method.

Keywords: Sliding mode control, Uncertain systems, LMIs
Abstract: In this paper, a new approach for designing a robust Discrete-time Sliding Mode Control (DSMC) is proposed for the uncertain discrete-time systems. To this end, an LMI approach is used to develop a new framework to design the linear sliding functions which are linear to the state. The LMI approach proposed in this paper is designed to deal with uncertain systems (matched and unmatched). It is well known that the finite sampling rate for the discrete-time systems leads to this fact that state move within a bound around the predetermined sliding surface referred to as quasi-sliding mode band. In this paper, this matter will be discussed in a new point of view and an innovative method will be used to obtain the ultimate bound on the system state.

Keywords: Sliding mode control, Uncertain systems, Nonlinear systems
Abstract: Any uncertain smooth multi-input multi-output dynamic system of a full relative degree can be locally finite-time stabilized at its equilibrium point by means of a standard continuous feedback, provided an approximation of the partial-derivatives’ matrix of highest order total output derivatives with respect to controls is available. Homogeneous sliding-mode approach is modified for this sake, and a list of controllers is built. Global finite-time stabilization is possible with a prescribed convergence-time function. The asymptotic output stabilization accuracies in the cases of discrete and noisy sampling can be adjusted in advance. Output-feedback controllers are constructed. Computer simulation confirms the applicability of the approach.

Keywords: Sliding mode control
Abstract: In this work, the performance of the real sliding mode is characterized with the notion of performance margins under the assumption that the real sliding motion presents a limit cycle with acceptable amplitude and acceptable frequency. The performance of sliding mode controllers, in real sliding motion, is improved by means of the addition of linear compensators in cascade connection with the plant. The applied compensators are phase lead controllers which modify the frequency response of the plant in order to meet the required performance margins adding robustness to the system. Bode diagram interpretation of performance margins is presented for the first time allowing the utilization of SMC combined with the classical methodology of linear compensator design where it is possible shape the Bode diagram in order to obtain desired values of performance margins. Examples supporting the proposed idea are presented.

Keywords: Linear parameter-varying systems, LMIs, Sampled data control
Abstract: This paper is concerned with the problem of discretization and discrete-time output feedback control design for polytopic continuous-time linear parameter-varying (LPV) systems with network-induced delay. Using a constant sampling period and an extension of the Taylor series expansion applied to the exponential of a parameter-dependent matrix, a discretized model whose matrices depend polynomially on the time-varying parameters that are used to schedule the control gain is obtained. The discrete-time model also has additive norm bounded terms, representing the discretization errors, and a network-induced delay in the control signal. A two-step strategy based on linear matrix inequality (LMI) conditions is then proposed to synthesize a digital static scheduled output feedback control law that stabilizes both the discretized and the original continuous-time LPV system. The conditions can also be used to provide robust (i.e., independent of the scheduling parameter) static output feedback controllers. The viability of the proposed design method is illustrated through a numerical example.

Keywords: Linear parameter-varying systems, Constrained control, LMIs
Abstract: This paper considers the stabilization issue for continuous-time linear parameter varying (LPV) positive systems. The time varying parameters are known and are modeled as belonging to the simplex set. The proposed stabilization approach relies on a parameter dependent Lyapunov function combined with a subtle choice of a slack variable that is not necessary diagonal. In fact, due to the positivity constraint on the closed-loop system the slack variable is chosen to be a Metzler matrix. Indeed, the particular case when the slack matrix is diagonal may work but the resulting stabilization conditions can be conservative. This fact is illustrated by a comparison example.

Keywords: Fault detection, Sliding mode control, Aerospace
Abstract: This paper presents a fault detection scheme for linear parameter varying (LPV) systems with uncertain or imperfectly measured scheduling parameters, using sliding mode observers (SMOs). In most LPV systems, it is assumed that the scheduling parameters are exactly known, but due to noise or inaccurate faulty sensors, it is sometimes not possible to know the scheduling parameters perfectly and a design based on nominal scheduling parameters cannot be guaranteed to work well in this situation. In this paper a SMO is proposed to reconstruct actuator faults in the situation where the scheduling parameters are imperfectly known. In this paper the observer gains are obtained from an linear matrix inequality optimisation and a rigorous error analysis. The efficacy of the proposed approach is demonstrated on RECONFIGURE actuator fault benchmark problem.

Keywords: Linear parameter-varying systems, Predictive control for linear systems, Stochastic optimal control
Abstract: The problem of controlling an LPV system subject to both hard and probabilistic constraints is considered. A necessary and sufficient condition for the inclusion of a polytope within another polytope, which is defined in terms of random variables, is given. This leads naturally to a tube MPC optimisation including linear probabilistic constraints. This can be solved approximately by considering a related problem obtained by sampling, which gives a mixed integer programming problem with a convex continuous relaxation. For fast sampling applications, we outline efficient approximate methods of solving the MIP via greedy constraint removal.

Keywords: Linear parameter-varying systems, Robust control, Optimization algorithms
Abstract: A robust synthesis algorithm is proposed for a class of uncertain linear parameter varying (LPV) systems. The uncertain system is described as an interconnection of a nominal (not-uncertain) LPV system and an uncertainty whose input/output behavior is described by an Integral Quadratic Constraint (IQC). The proposed algorithm is a coordinate-wise ascent that is similar to the well-known DK iteration for mu-synthesis. In the first step, a nominal controller is designed for the LPV system without uncertainties. In the second step, the robustness of the designed controller is evaluated and a new scaled plant for the next synthesis step is created. The robust performance condition used in the analysis step is formulated as a dissipation inequality that incorporates the IQC and generalizes the Bounded Real Lemma like condition for performance of nominal LPV systems. Both steps can be formulated as a semidefinite program (SDP) and efficiently solved using available optimization software. The effectiveness of the proposed method is demonstrated on a simple numerical example.

Keywords: Uncertain systems, Time varying systems, Switched systems
Abstract: In this paper robust stability of continuous-time linear time-varying systems is addressed based on Lyapunov functions which are constructed by max-composition of continuously differentiable functions. The resulting Lyapunov functions are continuous but not necessarily differentiable and no individual component needs to be positive definite. When the components are quadratic functions it will be possible to prove robust stability of systems which fail the classic quadratic stability test. The resulting conditions are matrix inequalities which are linear after choosing a set of tuning parameters. The robust stability condition is also extended to provide upper bounds on integral performance measures.

Keywords: Algebraic/geometric methods, Optimal control
Abstract: We prove, for real-analytic subriemannian metrics, that if a trajectory parametrized by arc-length is an arc-length minimizer then the trajectory is real-analytic on an open dense subset of its interval of definition.

Keywords: Algebraic/geometric methods, Nonlinear systems
Abstract: Transformation groups have been used extensively in system theory since its inception. Recently, a feedback transformation group for a nonlinear input-output system characterized by a Chen-Fliess functional expansion was described by the authors. In particular, an algorithm was given to identify a class of feedback invariant series. Their relationship to series having well-defined relative degree was also developed. This paper is a continuation of that work, but with three innovations. First, newly developed algebraic tools from the field of pre-Lie algebras are applied to give more insight into the invariance theory. The role of relative degree in this paper is diminished in favor of systems with arbitrary generating series. Finally, dynamic output feedback, as described by the feedback product, is considered explicitly.

Keywords: Algebraic/geometric methods, Nonlinear systems
Abstract: This paper provides a dendriform-tree setting for Fliess operators with matrix-valued inputs. This class of analytic nonlinear input-output systems is convenient, for example, in quantum control. In particular, a description of such Fliess operators is provided using planar binary trees. Sufficient conditions for convergence of the defining series are also given.

Keywords: Algebraic/geometric methods, Aerospace, Robotics
Abstract: A quaternion representation is often used to describe the attitude of a rigid body type spacecraft since it does not have any singular point whereas the conventional Euler angle description intrinsically has one. However, the dynamical equation with quaternions become more complicated than those described by Euler angles. In order to control the system with quaternions easily, we apply the authors' previous work on trajectory tracking control for port-Hamiltonian systems and extend it to handle quaternions. In the proposed design procedure, we do not need to solve any additional partial differential equations whereas nonlinear control very often requires to solve them.

Keywords: Algebraic/geometric methods, Lyapunov methods, Nonlinear systems
Abstract: This paper considers the problem of representing a sufficiently smooth control affine system as a structured potential-driven system and to exploit the obtained representation to study L₂-stability and stabilization. The representation problem has been studied extensively in recent years for particular classes of potential-driven systems, however exploiting these structures, for example generalized Hamiltonian systems, to study input-output stability was not fully investigated in the literature. The present note proposes a geometric decomposition technique, based on the Hodge decomposition theorem, to re-express a given vector field into a potential-driven form. Using the proposed decomposition technique, finite gain stability conditions are developed, in the form of Hamilton--Jacobi inequalities, based on the convexity of a computed potential.

Keywords: Algebraic/geometric methods, Modeling, Emerging control theory
Abstract: This paper addresses the problem of feedback invariance in geometric control theory by overviewing a framework that is inherently feedback-invariant. Crucial to the coherence of the method are suitable topologies on spaces of vector fields. The formulation also makes reference to the theory of presheaves and sheaves. While the work is addressed squarely at a fundamental problem of control theory, the technical background for the methods expounded upon are sometimes very complex. For this reason, the intent of the paper is to be expository, rather than technical.

Keywords: Energy systems, Optimization, Process Control
Abstract: This paper presents a methodology for the application of receding horizon optimization techniques to the problem of optimally managing the energy flows in the chlor-alkali process using a hybrid renewable energy system (HRES). The HRES consists of solar and wind energy generation units and fuel cells to supply electricity and heat. The HRES is also connected to the grid and allows for buying or selling electricity from and to the grid. Initially, detailed models of each system component are introduced as the basis for the simulation study. Energy management strategies are then developed to realize the objectives of meeting production requirements while minimizing the overall operating and environmental costs. Production demand response to maximize profits and load contracting to reduce uncertainties are also integrated into the proposed methodology.

Keywords: Energy systems, NL predictive control, Distributed control
Abstract: Nonlinear Model Predictive Control (NMPC) has been identified as a highly promising control technique for wind turbine generators, and has been shown to be real- time feasible for the control of individual wind turbines. The potential benefit of performing control at the wind farm level is well understood, and has been recently investigated in the literature. Likewise, the extension of NMPC from wind turbine to wind farm control is highly desirable, but very challenging since it requires solving large non-convex optimal control problems in real time. It has not been considered so far in the literature. This paper proposes a first contribution in that direction, using a distributed optimisation approach based on the Lagrange relaxation. The proposed algorithm requires a very limited amount of additional computations when compared to controlling the wind turbines individually via NMPC. The problem of smoothing the wind farm power output is considered here.

Keywords: Energy systems, Decentralized control, Predictive control for linear systems
Abstract: A decentralized model predictive controller (MPC) shows its higher efficacy than a centralized MPC scheme, especially when the number of controlled agents increases. In the smart grid, to realize load regulation using the demand side management idea, we present a decentralized MPC scheme for controlling the aggregated power output of thermostatically controller appliances (TCAs) to provide this service. Minimum ON/OFF time constraints, which are converted from logic conditions into inequalities, are modelled inherently in the optimization problem. A simulation using realistic data reveals the feasibility and efficacy of the proposed decentralized MPC scheme.

Keywords: Energy systems, Predictive control for linear systems
Abstract: We show how to construct the explicit solution to a model predictive control (MPC) problem which maintains optimal thermal comfort, represented by the Predicted Mean Vote (PMV) index, within required limits. Such an explicit solution allows the MPC policy to be implemented easily even in very simple building automation hardware. To cope with nonlinearity of the PMV index, we propose to linearize it while considering the linearization coefficients as time-varying parameters. Hence the explicit MPC controller is parameterized not only in state measurements, but also in coefficients of the linearization. Doing so mitigates the negative impact of linearization on control performance.

Keywords: Energy systems, Optimization, Optimal control
Abstract: In this paper we consider the problem of optimizing the operation of a building heating system under the hypothesis that the building is included as a consumer in a Demand Response program. Demand response requests to the building are assumed to come from an external market or grid operator. The requests assume the form of price/volume signals specifying a time duration, a volume of energy to be saved during a given time slot and a monetary reward assigned to the participant in case it fulfills the conditions. A receding horizon control approach is adopted for minimization of the energy bill, by exploiting a simplified model of the building. Since the resulting optimization problem is a mixed integer linear programming problem which turns out to be manageable only for buildings with few zones, a heuristic is devised to make the algorithm applicable to realistic size problems as well. The derived control law is tested on the realistic simulator EnergyPlus to evaluate pros and cons of the proposed algorithm. The performance of the suboptimal control law is evaluated by comparison with the optimal one on a chosen test case.

Keywords: Energy systems, Statistical learning, Closed loop identification
Abstract: A personalized control framework that tightly combines online learning of the energy consumer's utility function and the control of the consumer's electric loads according to real-time updates of the utility is proposed. This framework is particularly useful to automatically customize the controller of electric loads that directly affect the consumer's comfort. Because the utility function is identified and predicted online using Gaussian process regression, the controller is capable of immediately setting its objective function to the learned utility function and of adjusting its control action to maximize the new objective. Furthermore, no separate training period to learn the consumer's utility is needed. The performance of the proposed method is demonstrated by the application to a personalized thermostat controlling indoor temperature.

Keywords: Emerging control applications, Optimization, Network analysis and control
Abstract: With the increasing popularity and ubiquity of online social networks (SNS), many advertisers choose to post their advertisements (Ads) within SNS. As a central problem for Ad platforms, Ad allocation is to maximize its revenue without overcharging advertisers, and it has received increasing attention from both industry and academia. The offline approach is a high dimensional integer programming problem with constraints incorporating potential allocation requirements from advertisers. In this paper we investigate the SNS Ad allocation problem in a single target group setting, study the connection of SNS advertising and hyperbolic geometry, and propose an approximation using hyperbolic embedding, which not only reduces the dimensionality of SNS Ad allocation problem significantly, but also provides a general framework for designing allocation strategies incorporating business rules. We evaluate the optimality and efficiency of our approach.

Keywords: Emerging control applications, Predictive control for linear systems
Abstract: In this work, we propose to expand the application of model predictive control (MPC) to problems in which there are human agents involved in the sensing and actuation processes. To this end, a new configuration of a control system structure that combines centralized predictive control and local operations is presented. Additional constraints are included in the optimization problem to take into account the mobility and the role of the operators over the prediction horizon. This new type of control system structure, referred to as Mobile Model Predictive Control (MoMPC), is tested on a linear model of a large scale irrigation canal and its performance is compared to centralized MPC and manual operation.

Keywords: Manufacturing
Abstract: Production lead time (LT) is the average time a part spends in the system, being processed and waiting for processing. Some recent work provided methods for analysis of LT in systems with machines obeying the Bernoulli reliability model. Since this reliability model is hardly applicable to machining and other operations with a relatively long downtime, the current paper addresses serial lines with exponential machines and infinite buffers. Specifically, analytical formulas for LT as a function of machine parameters are derived, and qualitative and quantitative properties of LT are investigated. Using these formulas, the so-called lead time control problem is solved, whereby the raw material release rate is selected so that LT takes the desired value, while the throughput is maximized. Both open- and closed-loop solutions of this problem are provided.

Keywords: Emerging control applications, Energy systems, Aerospace
Abstract: A study on the aerodynamics and on the active pitch control of curved tethered wings for airborne wind energy is presented. Computational fluid dynamics techniques, previously validated with experimental data, are used to derive the aerodynamic coefficients of a curved kite as a function of the angle of attack. In contrast with previous results, such analysis indicates that the kite efficiency is quite flat over a wide range of values of the angle of attack. Based on such analysis, an active pitch control strategy is proposed, which is able to maximize the generated traction force during operation without requiring neither an estimate of the angle of attack, nor an accurate model of the system’s dynamics.

Keywords: Emerging control applications, Machine learning, Intelligent systems
Abstract: The interaction based on gestures has become a prominent approach to interact with electronic devices. In this paper a Machine Learning (ML) based approach to gesture recognition (GR) is illustrated; the proposed tool is freestanding from user, device and device orientation. The tool has been tested on a heterogeneous dataset representative of a typical application of gesture recognition. In the present work two novel ML algorithms based on Sparse Bayesian Learning are tested versus other classification approaches already employed in literature (Support Vector Machine, Relevance Vector Machine, k-Nearest Neighbor, Discriminant Analysis). A second element of novelty is represented by a Principal Component Analysis-based approach, called Pre-PCA, that is shown to enhance gesture recognition with heterogeneous working conditions. Feature extraction techniques are also investigated: a Principal Component Analysis based approach is compared to Frame-Based Description methods.

Keywords: Emerging control applications, Uncertain systems, Randomized algorithms
Abstract: We consider the problem of minimizing the electric energy consumption in the climate control of a building. More specifically, we suppose that the reference temperature in the building can be modulated to some extent during the day, so as to reduce the power request while limiting the introduced level of discomfort. To account for the uncertain building occupancy, we formulate the optimal energy management problem as a chance constrained optimization problem where one seeks for a state feedback policy that is robust over all occupancy realizations except for a set of predefined (small) probability. By exploiting the different time scales of the control and disturbance inputs, an algorithmic solution based on nested dynamic programming and randomized optimization is put forward and its parallel GPU implementation is discussed. A numerical example shows the efficacy of the approach.

Keywords: Machine learning, Aerospace, Traffic control
Abstract: We extend the maximum causal entropy framework for inverse reinforcement learning to the infinite time horizon discounted reward setting. To do so, we maximize discounted future contributions to causal entropy subject to a discounted feature expectation matching constraint. A parameterized class of stochastic policies that solve this problem are referred to as soft Bellman policies because they can be specified in terms of values that satisfy an equation identical to the Bellman equation but with a softmax (the log of a sum of exponentials) instead of a max. Under some assumptions, algorithms that repeatedly solve for a soft Bellman policy, evaluate the policy, and then perform a gradient update on the parameters will find the optimal soft Bellman policy. For the first step, we extend techniques from dynamic programming and reinforcement learning so that they derive soft Bellman policies. For the second step, we can use policy evaluation techniques from dynamic programming or perform Monte Carlo simulations. We compare three algorithms of this type by applying them to a problem instance involving demonstration data from a simple controlled queuing network model inspired by problems in air traffic management.

Keywords: Machine learning, Optimization, Distributed control
Abstract: This paper presents an electric vehicle (EV) charging algorithm based on regret minimization. While many distributed algorithms for EV charging have been proposed, many of them implicitly assume low-latency two-way communication between the distribution company and the EV customers. This assumption is limiting at present. Furthermore, transmission of information about total load and planned charging schedules also raises concerns of security and privacy. The proposed algorithm resolves these issues at the expense of slower convergence to the optimal solutions. The algorithm considers a relaxation of the problem in the sense that the charging profiles are sought to be optimized over the set of profiles that do not vary from one day to the next. The proposed method only requires communication in the form of the distribution company publishing the pricing profiles implemented for the previous days. We provide convergence results for the algorithm and illustrate the results through numerical examples.

Keywords: Machine learning, Optimization, Nonlinear systems
Abstract: We study the min max optimization problem introduced in [Fonteneau et al. (2011), ``Towards min max reinforcement learning'', Springer CCIS, vol. 129, pp. 61-77] for computing control policies for batch mode reinforcement learning in a deterministic setting with fixed, finite optimization horizon. First, we state that the min part of this problem is NP-hard. We then provide two relaxation schemes. The first relaxation scheme works by dropping some constraints in order to obtain a problem that is solvable in polynomial time. The second relaxation scheme, based on a Lagrangian relaxation where all constraints are dualized, can also be solved in polynomial time. We theoretically show that both relaxation schemes provide better results than those given in [Fonteneau et al. (2011)].

Keywords: Machine learning, Predictive control for linear systems, Optimization algorithms
Abstract: A new type of parametrizations is proposed which allows to reduce the size of the online optimization in linear MPC. The parametrizations combine a first part ensuring feasibility and asymptotic stability of the closed loop and a second part promoting performance. The performance promoting part is determined a priori offline based on a data mining algorithm which has been introduced in our previous work. In comparison to this work, the new results provide full flexibility in the choice of training data and thereby allow application of the method to larger problems. This is verified in two numerical examples which illustrate the benefits of the new method.

Keywords: Machine learning, Statistical learning, Markov processes
Abstract: In this paper we propose an approach for unsupervised Inverse Reinforcement Learning (IRL) with noisy data using a hidden variable Markov Decision Processes (hMDP) representation. hMDP accounts for observation uncertainty by using a hidden state variable. We develop a nonparametric Bayesian IRL technique for hMDP based on Dirichlet Processes mixture model. We provide an efficient Markov Chain Monte Carlo based sampling algorithm whereby one can automatically cluster noisy data into different behaviors, and estimate the underlying reward parameters per cluster. We demonstrate our approach for unsupervised learning, and prediction and classification of agent behaviors in a simulated surveillance scenario.

Keywords: Intelligent systems, Machine learning
Abstract: In cluster analysis, distinguishing abnormal behavior from noise is an important problem that has remained unresolved for many years. This paper presents a general approach for distinguishing abnormal behavior from noise and for identifying abnormal behavior in noisy data sets. The approach is an application of a new, complete linkage hierarchical clustering method for n(n-1)/2 + 1-level hierarchical sequences and a means for finding meaningful levels of such hierarchical sequences prior to performing a cluster analysis. These technologies were designed with small-n, large-m data sets in mind. Based on four broadly applicable assumptions, the approach uses higher dimensionalities to reveal inherent structure in noisy data sets and find meaningful levels in the corresponding hierarchical sequences. The new clustering method is used to construct only the cluster sets that correspond to these levels. Results from a first experiment show how the effects of noise are attenuated as the dimensionality of the data points increases. Results from a second experiment show how meaningful cluster sets can have real world meanings that are useful for identifying abnormal behavior.

Keywords: Fault diagnosis, Fault tolerant systems, Predictive control for linear systems
Abstract: In this paper, a sensor fault-tolerant control (FTC) scheme using min-max robust model predictive control (MPC) and set-theoretic fault detection and isolation (FDI) is proposed. The MPC controller is used to both robustly control the plant and actively guarantee fault isolation (FI) conditions. In this scheme, fault detection (FD) is passive by interval observers, while fault isolation (FI) is active by MPC and sets. The advantage of the proposed approach consists in using MPC to actively decouple the effect of sensor faults on the outputs such that one output component only corresponds to one sensor fault. In this way, the proposed FI approach can make good use of the features of sensor faults. A numerical example is used to illustrate the effectiveness of the proposed approach.

Keywords: Fault diagnosis, Fault tolerant systems, Predictive control for linear systems
Abstract: In this paper, an actuator fault-tolerant control (FTC) scheme is proposed, which is based on tube-based model predictive control (MPC) and set-theoretic fault detection and isolation (FDI). As a robust MPC technique, tube-based MPC, can effectively deal with system constraints and uncertainties with relatively low computational complexity. Set-based FDI can robustly detect and isolate actuator faults. Here, fault detection (FD) is passive by invariant sets, while fault isolation (FI) is active by tubes. Using the constraint-handling ability of MPC controllers, an active FI approach is implemented. A numerical example illustrates the effectiveness of the proposed approach.

Keywords: Fault tolerant systems, Aerospace, Lyapunov methods
Abstract: This paper addresses the attitude tracking control problem of spacecraft in the presence of sign errors in actuator response which are uncertain in occurring time instants and patterns. Either a software or hardware fault may cause such an actuation sign error which will lead to the system instability even loss of spacecraft. A multiple-model control scheme, consisted of a bank of controllers and a control switching mechanism, is developed to compensate such actuation sign errors and to ensure the system stability and asymptotic attitude tracking properties. Simulation results are presented to verify the performance of the proposed multiple-model control scheme.

Keywords: Fault tolerant systems, Constrained control, Stability of NL systems
Abstract: This paper focuses on fault tolerant control allo- cation for overactuated systems with actuator dynamics. The proposed scheme for fault detection and isolation is based on unknown input observers and the main contribution of the paper consists in the presentation of a finite-time control re- configuration technique which provides a successful recovering of system performances in spite of actuator faults. Simulation results support theoretical developments.

Keywords: Fault tolerant systems, NL predictive control, Distributed control
Abstract: This paper deals with a novel Plug-and-Play (PnP) architecture for the control and monitoring of Large-Scale Systems (LSSs). The proposed approach integrates a distributed Model Predictive Control (MPC) strategy with a distributed Fault Detection (FD) methodology for a class of nonlinear LSS in a PnP framework. The basic concept is to use the FD scheme as an autonomous decision support system: once a fault is detected, the faulty subsystem can be unplugged to avoid the propagation of the fault in the interconnected LSS. Analogously, once the issue has been solved, the disconnected subsystem can be re-plugged-in. PnP design of local controllers and detectors allow these operations to be performed safely, i.e. without spoiling stability and constraint satisfaction for the whole LSS.

Keywords: Fault tolerant systems, Robust control, Optimization
Abstract: This paper presents a fault-tolerant control allocation scheme for overactuated spacecraft attitude tracking systems subject to actuator faults. Taking the effect of fault detection and diagnosis (FDD) uncertainties into account, a performance/robustness tradeoff control allocation (PRTCA) strategy is proposed to redistribute the virtual control signals to the remaining actuators without reconfiguring the controller. The proposed PRTCA scheme achieves robustness with respect to the imprecise in fault estimation, and is less conservative than the robust control allocation. To illustrate the performance of the proposed PRTCA strategy, numerical simulations are carried out for a rigid spacecraft in the presence of reaction wheel faults.

Keywords: Kalman filtering, Communication networks, Filtering
Abstract: Some important textbooks on Kalman Filters suggest that positive semidefinite solutions to the filtering Algebraic Riccati Equation (ARE) cannot be stabilizing should the underlying state variable realization be unstabilizable. We show that this is false. Questions of uniqueness of positive semidefinite solutions of the ARE are also unresolved in the absence of stabilizability. Yet fundamental performance issues in modern communications systems hinge on Kalman Filter performance absent stabilizability. In this paper we provide a positive semidefinite solution to the ARE for detectable systems that are not stabilizabile and show that it is unique if the only unreachable modes are on the unit circle.

Keywords: Kalman filtering, Estimation, Filtering
Abstract: This paper concerns the state estimation problem for linear discrete-time systems with non-Gaussian state and output noises. A sub-optimal quadratic filter algorithm is proposed. In order to enlarge the class of systems allowed to be processed, a novel approach based on the output injection stabilization is derived. Also a second benefit to the estimate performances, due to the possibility of assignment of the system eigenvalues, is investigated. Numerical results validate the effectiveness of the proposed method.

Keywords: Kalman filtering, Estimation, Linear system observers
Abstract: Censored measurements arise frequently in engineering applications in the form of saturation, limit of detection, and occlusion effects. Censored data regression uses a formulation known as the Tobit model. We have recently presented a novel extension of the Kalman filter that allows for optimal state tracking in the presence of censored measurements. We call this formulation the Tobit Kalman filter. In this paper, we present an application of the Tobit Kalman filter to mobile vehicle position estimation using received signal strength from a number of antennas. Received signal strength drops below the noise floor as distance increases, and is therefore a censored measurement. We will briefly introduce the Tobit Kalman filter and compare its performance on the position estimation problem with the standard Kalman filter. Stable closed-loop control will be demonstrated by use of the Tobit Kalman filter as an observer in a linear-quadratic-Gaussian regulator.

Keywords: Kalman filtering, Estimation, LMIs
Abstract: The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman filter. The main difference of the proposed filter from the conventional extended Kalman filter is in the use of a computed mean square error bound matrix, to calculate the filter gain, and to serve as bound on the actual mean square error. The paper shows that when the system is linear the proposed filtering algorithm reduces to the conventional Kalman filter. The theory presented in the paper is applicable to a wide class of systems, but if the system is polynomial, then the recently developed theory of positive polynomials considerably simplifies the filter's implementation.

Keywords: Kalman filtering, Estimation, Nonlinear systems
Abstract: In order to improve vehicle's active safety systems accurate knowledge about the vehicle's driving stability is necessary. Especially the exact determination of the side-slip angle can be of great importance, since it has major potential for improving current control algorithms. Therefore, a model-based methodology for online estimation of vehicle's lateral dynamics is presented, while generalizations of the Kalman Filter algorithm, the Extended and Unscented Kalman Filters are used due to the highly non-linear model behavior. The results of the introduced methodologies are presented for two different driving maneuvers and validated comparing to measurements taken with a VW Golf GTI. Furthermore, a qualitative comparison between Extended and Unscented Kalman Filter is realized.

Keywords: Kalman filtering, Filtering
Abstract: This paper addresses the problem of optimal state estimation (OSE) for a wide class of nonlinear time series models. Empirical evidence suggests that the Unscented Kalman Filter (UKF), proposed by Julier and Uhlman, is a promising technique for OSE with satisfactory performance. Unscented Transformation (UT) is the central and vital operation performed in UKF. A crucial point of UT is to construct a sigma-set, which consists of points with associated weights capturing the input statistics, e.g., first and second and possibly higher moments. We analyze the standard choice of sigma-set and propose a novel method for generating sigma-set so as to capture arbitrary higher order input statistics. This method could be considered as a linear extension of UT or UKF, and its computational complexity is the same order as that of the UKF and so EKF. The performance of the algorithm is illustrated by empirical examples. Results show an improvement in accuracy compared to traditional UKF.

Keywords: Optimization algorithms, Electrical power systems, Large-scale systems
Abstract: The increased presence of Electric Vehicles (EVs) within electricity distribution systems introduces new challenges to their reliability, since uncoordinated charging of large numbers of EV can result in overload of distribution lines or transformers. In order to manage this difficulty, entities called EV aggregators are introduced whose task is to schedule charging of the EV fleet while ensuring that network constraints are respected. In this paper we propose a solution method for the type of constrained optimization problems such aggregators must solve. Our method is simple to implement and is guaranteed to produce good and feasible solutions, while performing only lightweight centralized computations which do not require the use of additional – and often expensive – constrained optimization solvers. We show that the quality of solutions produced by our method improves as the number of EVs to be controlled is increased. In addition, the computation times remain very short even for large problem instances entailing several thousands EVs.

Keywords: Optimization algorithms, Optimization
Abstract: The performance of Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) (i.e. Douglas-Rachford splitting on the dual problem) are sensitive to conditioning of the problem data. For a restricted class of problems that enjoy a linear rate of convergence, we show in this paper how to precondition the optimization data to optimize a bound on that rate. We also generalize the preconditioning methods to problems that do not satisfy all assumptions needed to guarantee a linear convergence. The efficiency of the proposed preconditioning is confirmed in a numerical example, where improvements of more than one order of magnitude are observed compared to when no preconditioning is used.

Keywords: Optimization algorithms, Optimization
Abstract: First order optimization methods often perform poorly on ill-conditioned optimization problems. However, by preconditioning the problem data and solving the preconditioned problem, the performance of the first order method can be significantly improved. In this paper, we show how to compute such preconditioners when solving the dual of strongly convex optimization problems using fast dual proximal gradient methods. The proposed preconditioning is evaluated by solving ill-conditioned optimization problems that arise from controlling the pitch angle in an aircraft using model predictive control. The numerical example shows improvements of two to three orders of magnitude in the fast dual proximal gradient method compared to when no preconditioning is used.

Keywords: Optimization algorithms, Optimization
Abstract: Consider a set of networked agents endowed with private cost functions and seeking to find a consensus on the minimizer of the aggregate cost. The Alternating Direction Method of Multipliers (ADMM) has shown to be particularly efficient to solve this kind of problem. In this paper, we assume that there exists a unique minimum and that the cost functions are twice differentiable at the minimum and verify a local strong convexity assumption. Under these assumptions, we prove the linear convergence of the distributed ADMM to the consensus over the sought minimum and derive a tight convergence rate. Finally, we give examples where one can derive the ADMM hyper-parameter corresponding to the optimal rate.

Keywords: Optimization algorithms, Optimization, NL predictive control
Abstract: A novel splitting scheme to solve parametric multi-convex programs is presented. It consists of a fixed number of proximal alternating minimisations and a dual update per time step, which makes it attractive in a real-time Nonlinear Model Predictive Control (NMPC) framework and for distributed computing environments. Assuming that the parametric program is semi-algebraic and that its critical points are strongly regular, a contraction estimate is derived and it is proven that the suboptimality error remains stable under some mild assumptions. Efficacy of the method is demonstrated by solving a bilinear NMPC problem to control a DC motor. In particular, the effect of the sampling period on the optimality tracking error is analysed for a fixed computational power.

Keywords: Optimization algorithms, Optimization
Abstract: Fast gradient methods are known to be non-monotone algorithms, and oscillations typically occur around the solution. To avoid this behavior, we propose in this paper a fast gradient method with restart, and analyze its convergence rate. The proposed algorithm bears similarities to other algorithms in the literature, but differs in a key point that enables theoretical convergence rate results. The efficiency of the proposed method is demonstrated by two numerical examples.

Keywords: Optimal control, Algebraic/geometric methods, Variational methods
Abstract: The problem of recovering continuous time signals from a set of discrete measurements is ill-posed in a classical sense (non-uniqueness of solution). Our approach introduces generative models with inputs, states and outputs, and regularizes this problem by trading total fit-error against suitable penalty functionals of input and state. This enables us to apply techniques from optimal control and obtain solutions in a semi-analytical way. Using a modified version of Pontryagin’s maximum principle, this paper treats data smoothing as an optimal control problem. In addition to addressing data smoothing problems in Euclidean settings, our results are also applicable to problems arising in finite dimensional matrix Lie group settings. In particular, this paper discusses an example problem on SE(2), and exploits symmetry and reduction to an integrable Hamiltonian system as means to data smoothing.

Keywords: Optimal control, Linear systems, Hybrid systems
Abstract: Linear systems described by hybrid dynamics are considered; that is systems described by linear time-varying models with continuous control inputs as well as "jump" dynamics at discrete time instants where impulsive control inputs are applied. A quadratic performance index is formulated and the necessary conditions for optimality are determined using variational calculus. The solution to the control problem is obtained using two types of Riccati equations: the usual continuous-time Riccati differential equation and a discrete Riccati equation which yields discontinuous jumps in the continuous-time solution. Necessary and sufficient conditions for optimal timing of the impulsive inputs are also presented. Numerical examples are provided which demonstrate the correctness of the solutions.

Keywords: Optimal control, Lyapunov methods, Nonlinear systems
Abstract: In this paper, we propose a data-driven optimal feedback controller design method based on approximate value iteration which is a kind of dynamic programming method. With the data set containing sufficient dynamic information of the plant, the data-driven dynamic programming operator is well defined. An approximate of the optimal cost function is obtained by successively using the data-driven dynamic programming operator on a initial function. Based on the approximate of the optimal cost function, a sub-optimal controller is designed. The data used in data-driven dynamic programming operator belongs to the data subset, whose elements make the difference of a positive-definite function to be negative-definite. Hence, the stability of the closed-loop is guaranteed. Because the controller is designed directly from data, complexity in building the model and modeling error are avoided.

Keywords: Machine learning, Optimal control, Adaptive control
Abstract: This paper provides an approximate online adaptive solution to the infinite-horizon optimal tracking problem for control-affine continuous-time nonlinear systems with unknown drift dynamics where model-based reinforcement learning is used to relax the persistence of excitation condition. Model-based reinforcement learning is implemented using a concurrent learning-based system identifier to simulate experience by evaluating the Bellman error over unexplored areas of the state space. Tracking of the desired trajectory and convergence of the developed policy to a neighborhood of the optimal policy is established via Lyapunov-based stability analysis.

Keywords: Optimal control, NL predictive control, Optimization
Abstract: Receding horizon control is a type of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. Implicit systems belong to a more generalized class of systems than a class of explicit systems, because they can additionally contain algebraic constraints. The objective of this study is to develop a novel design method of receding horizon control for a generalized class of discrete-time nonlinear implicit systems. Using the variational principle, we derive the stationary conditions that must be satisfied for a performance index to be optimized. Moreover, we provide numerical algorithms for solving the obtained stationary conditions. Next, we establish the stability criterion for the closed-loop system with the proposed method. Finally, the effectiveness of the proposed method is verified by numerical simulations.

Keywords: Optimal control, Nonlinear systems, Adaptive control
Abstract: Adaptive dynamic programming is applied to control-affine nonlinear systems with uncertain drift dynamics to obtain a near-optimal solution to a finite-horizon optimal control problem with hard terminal constraints. A reinforcement learning-based actor-critic framework is used to approximately solve the Hamilton-Jacobi-Bellman equation, wherein critic and actor neural networks (NN) are used for approximate learning of the optimal value function and control policy, while enforcing the optimality condition resulting from the hard terminal constraint. Concurrent learning-based update laws relax the restrictive persistence of excitation requirement. A Lyapunov-based stability analysis guarantees uniformly ultimately bounded convergence of the enacted control policy to the optimal control policy.

Keywords: Large-scale systems, Game theory
Abstract: Constrained charging control of large populations of Plug-in Electric Vehicles (PEVs) is addressed using mean field game theory. We consider PEVs as heterogeneous agents, with different charging constraints (plug-in times and deadlines). The agents minimize their own charging cost, but are weakly coupled by the common electricity price. We propose an iterative algorithm that, in the case of an infinite population, converges to the Nash equilibrium associated with a related decentralized optimization problem. In this way we approximate the centralized optimal solution, which in the unconstrained case fills the overnight power demand valley, via a decentralized procedure. The benefits of the proposed formulation in terms of convergence behavior and overall charging cost are illustrated through numerical simulations.

Keywords: Large-scale systems, Distributed control, Delay systems
Abstract: We consider a class of large scale linear-quadratic coordination problems where the information exchange is subject to a time delay. We show that several previously known properties of the optimal solution to the delay-free problem extend to this case. In particular, the optimal control law comprises a diagonal (decentralized) term complemented by a rank-one coordination term, which can be implemented by a simple averaging operation. Moreover, the computational effort required to obtain the controller is independent of the number of agents.

Keywords: Emerging control theory, Linear systems, Large-scale systems
Abstract: In this paper, we study the control of the class of time-invariant linear ensemble systems, whose natural dynamics vary linearly with the system parameter. This class of ensemble control systems arises from practical engineering and physical applications, such as transport of quantum atoms and steering of uncertain harmonic systems. We, in particular, consider the ensemble systems with strictly positive or negative parameter values and derive explicit necessary and sufficient controllability conditions, which %is a rank condition and is are easy to be checked. Our derivation is based on the notion of polynomial approximation, where the elements of the reachable set are represented in polynomials of the system parameter and used to approximate the desired state of interest. In addition, we highlight the role of the spectra of the system matrices play in the determination of ensemble controllability. Illustrative examples with numerical simulations are provided to demonstrate the tractability of the developed controllability conditions.

Keywords: Large-scale systems, Networked control systems, Distributed control
Abstract: In this paper, we develop a novel unified methodology for performance and robustness analysis of linear dynamical networks. We introduce the notion of systemic measures for the class of first-order linear consensus networks. We classify two important types of performance and robustness measures according to their functional properties: convex systemic measures and Schur-convex systemic measures. It is shown that a viable systemic measure should satisfy several fundamental properties such as homogeneity, monotonicity, convexity, and orthogonal invariance. In order to support our proposed unified framework, we verify functional properties of several existing performance and robustness measures from the literature and show that they all belong to the class of systemic measures. Moreover, we introduce new classes of systemic measures based on (a version of) the well-known Riemann zeta function, input-output system norms, and etc. Then, it is shown that for a given linear dynamical network one can take several different strategies to optimize a given performance and robustness systemic measure via convex optimization. Finally, we characterized an interesting fundamental limit on the best achievable value of a given systemic measure after adding some certain number of new weighted edges to the underlying graph of the network.

Keywords: Large-scale systems, Transportation networks, Network analysis and control
Abstract: Dynamical flow networks with heterogeneous routing are analyzed in terms of stability and resilience to perturbations. Particles flow through the network and, at each junction, decide which downstream link to take on the basis of the local state of the network. Differently from single-commodity scenarios, particles belong to different classes, or commodities, with different origins and destinations, each reacting differently to the observed state of the network. As such, the commodities compete for the shared resource that is the flow capacity of each link of the network. This implies that, in contrast to the single-commodity case, the resulting dynamical system is not monotone, hence harder to analyze. It is shown that, in an acyclic network, when a feasible globally asymptotically stable aggregate equilibrium exists, then each commodity also admits a unique equilibrium. In addition, a sufficient condition for stability is provided. Finally, it is shown that, differently from the single-commodity case, when this condition is not satisfied, the possible unique equilibrium may be arbitrarily fragile to perturbations of the network.

Keywords: Large-scale systems, Nonlinear systems, Optimization
Abstract: We present a compositional performance certification method for interconnected nonlinear systems, using dissipativity properties of the subsystems along with the interconnection structure. To select the most relevant dissipativity properties, we formulate a large-scale optimization problem, and solve it with the alternating direction method of multipliers (ADMM). The dissipativity properties are allowed to depend on an unknown equilibrium, enabling us to certify performance without explicit knowledge of the equilibrium for the interconnected system. The effectiveness of the algorithm is demonstrated on two examples, including a model of vehicle platoons.

Keywords: Discrete event systems, Autonomous robots, Petri nets
Abstract: This research proposes an automated method for planning a team of mobile robots such that a Boolean-based mission is accomplished. The specification consists of logical requirements over some regions of interest for the agents' trajectories and for their final states. A Petri net (PN) with outputs models the movement capabilities of the team and the active regions of interest. The imposed specification is translated to a set of linear restrictions for some binary variables, the robot movement capabilities are formulated as linear constraints on PN markings, and the evaluations of the binary variables are linked with PN markings via linear inequalities. This allows us to solve a Mixed Integer Linear Programming problem whose solution yields robotic trajectories satisfying the task.

Keywords: Discrete event systems, Petri nets, Linear systems
Abstract: This paper presents an integrated control strategy solving disturbance decoupling of max-plus linear systems. The classical disturbance decoupling problem (DDP) in geometric control theory means that the controlled outputs will not be changed by any disturbances. The DDP problem has no practical meaning in the context of Max-plus system, since the subtraction operation does not exist. The new proposed modified disturbance decoupling problem (MDDP) ensures that the controlled output signals will not be delayed more than the existing delays caused by the disturbances in order to achieve the just-in-time optimal control. Furthermore, this paper presents the integration of state-feedback and open-loop control strategies to solve the MDDP, as well as the DDP if possible. If the integrated control could not possibly solve the DDP, then an evaluation principle is established to compare the distance between the output signals generated by the controllers and the output signals generated by the disturbances. The main results of this paper are illustrated by a high throughput screening system in drug discovery.

Keywords: Discrete event systems, Supervisory control, Automata
Abstract: In this paper we present a new approach to decentralized supervisory control of large automata with communicating supervisors. We first generalize the recently developed top-down architecture of multilevel coordination control with a hierarchical structure of groups of subsystems, their respective coordinators and supervisors. Namely, in the case where the equivalent conditions for achieving a specification language fail to be satisfied, we propose sufficient conditions for a distributed computation of the supremal achievable sublanguage. We then apply the obtained constructive results of multilevel coordination control to decentralized supervisory control with communication, where local supervisors of subsystems within a group communicate with each other via the coordinator of the group. Our approach is illustrated by an example.

Keywords: Discrete event systems, Supervisory control, Automata
Abstract: We present new results on the synthesis of safe, non-blocking, and maximally permissive supervisors for partially observed discrete event systems. We consider the case where the legal language is a non-prefix-closed sublanguage of the system language and non-blockingness must be ensured in addition to safety. Our approach is based on the construction of a new bipartite transition system, called the Non-blocking All Inclusive Controller (NB-AIC), that embeds all safe and non-blocking supervisors. We present an algorithm for the construction of the NB-AIC and discuss its properties. We then provide a synthesis algorithm, based on the NB-AIC, that constructs a supervisor that is safe, non-blocking and maximally permissive. This is the first algorithm with such properties.

Keywords: Supervisory control, Genetic regulatory systems
Abstract: Controlling the behavior of intracellular networks has many important applications in Biotechnology and Medicine. In a previous work, we showed how the ideas from Supervisory Control Theory could be used to solve the state attraction problem applied to biological cells, i.e. guiding a cell from an initial state to some target state. The devised supervisor is then implemented by means of synthetic genes that are inserted in the cell. In this paper, we borrow ideas from Optimal Supervisory Control Theory to obtain supervisors that minimize an important metric associated with the problem of controlling the behavior of intracellular networks, namely, the minimization of the energy consumed for protein synthesis along the path from the initial to the target state.

Keywords: Supervisory control, Machine learning
Abstract: Sequential composition is an effective approach to address the control of complex dynamical systems. However, it is not designed to cope with unforeseen situations that might occur during runtime. This paper extends sequential composition control via learning new policies. A learning module based on reinforcement learning is added to the traditional sequential composition that allows for the online creation of new control policies in a short amount of time, on a need basis. During learning, the ac{DOA} of the new control policy is continuously monitored. Hence, the learning process only executes until the supervisor is able to compose the new control policy with designed controllers via the overlap of ac{DOA}s. Estimating the ac{DOA}s of the learned controllers is achieved by solving an optimization problem. The proposed strategy has been simulated on a nonlinear system. The results show that the learning module can rapidly augment the designed sequential composition by new control policies such that the supervisor could handle unpredicted situations online.

Keywords: Optimization algorithms, Randomized algorithms, Uncertain systems
Abstract: We propose efficient techniques for generating independent identically distributed uniform random samples inside semialgebraic sets. The proposed algorithm leverages recent results on the approximation of indicator functions by polynomials to develop acceptance/rejection based sample generation algorithms with guaranteed performance in terms of rejection rate (the number of samples that should be generated in order to obtain an accepted sample). Moreover, the {acceptance} rate is shown to be is asymptotically optimal, in the sense that it tends to one (all samples accepted) as the degree of the polynomial approximation increases. The performance of the proposed method is illustrated by a numerical example.

Keywords: Randomized algorithms, Computational methods, Markov processes
Abstract: This paper revisits the problem of particle uncertainty characterization and propagation for deterministic nonlinear continuous time dynamical systems. A revealing comparison is made between the traditional Monte Carlo method and a recently developed particle framework based on Markov chain Monte Carlo and the method of characteristics (MCMC-MOC). The focus is on dynamical systems that do not admit stationary solutions that often pose bigger problems for the Liouville equation than systems with fixed points. We demonstrate through dispersion analysis that while traditional Monte Carlo is unable to propagate the state density function in a statistically consistent manner and suffers from degeneracy, the MCMC-MOC approach performs very well. The new approach automatically extracts the domain of significance (support) of the state density function by constructing a Markov Chain guided by the solution of the stochastic Liouville equation. Being equivalent in measure to the true state probability density, the particles in the Markov chain can be used directly to compute desired expectations. Simple examples are used to illustrate the potential pitfalls of using traditional Monte Carlo and the corresponding advantages of the MCMC-MOC technique.

Keywords: Randomized algorithms, Uncertain systems, Optimization
Abstract: Stochastic approximation algorithms (for example SPSA) provide a way to solve optimization problems in the presence of arbitrary but bounded disturbances. In this paper a problem of position estimation for a moving point using monocular projective observations is considered. We add random pertrubations to camera position to produce an algorithm which makes estimates of point position demanding only that the point's velocity is bounded in time. This is superior to the methods currently available in the computer vision field which all consider very restricted cases of point movement (constant, movement in plane). We prove theoretical convergence of estimates and provide numerical simulation for the algorithm.

Keywords: Randomized algorithms, Electrical power systems, Optimization
Abstract: Robust optimal power flow problem is to find the optimal operating setting of a power system subject to some constraints based on power and voltage for any uncertain power generation. Since this problem is NP hard due to its nonconvexity, a computationally cheap randomized algorithm is presented. The algorithm is applied for the New England test system and its efficiency is demonstrated through numerical examples.

Keywords: Randomized algorithms, Predictive control for linear systems, Energy systems
Abstract: Improving energy efficiency of Heating, Ventilation and Air Conditioning (HVAC) systems is a primary objective for the society. Model Predictive Control (MPC) techniques for HVAC systems have recently received particular attention, since they can naturally account for several factors, such as weather and occupancy forecasts, comfort ranges and actuation constraints. Developing effective MPC based control strategies for HVAC systems is nontrivial, since buildings dynamics are nonlinear and affected by various uncertainties. Further, the complexity of the MPC problem and the burden of on-line computations can lead to difficulties in integrating this scheme into a building management system. We propose to address this computational issue by designing a scenario-based explicit MPC strategy, i.e., a controller that is simultaneously based on explicit representations of the MPC feedback law and accounts for uncertainties in the occupancy patterns and weather conditions by using the scenarios paradigm. The main advantages of this approach are the absence of a-priori assumptions on the distributions of the uncertain variables, the applicability to any type of building, and the limited on-line computational burden, enabling practical implementations on low-cost hardware platforms. We illustrate the practical implementation of the proposed explicit MPC controller on a room of a university building, showing its effectiveness and computational tractability.

Keywords: Randomized algorithms, Computational methods
Abstract: Many algorithms in numerical analysis, operations research, and control theory can be written as fixed point iterations of contraction maps. Because these algorithms are so pervasive, there is significant value in being able to perform these computations with lower computational latency. Previous work has focused on reducing the computational complexity of certain algorithms, but there has been less of a focus on using massively parallel computing systems to reduce computational latency. The rise of parallel computing systems makes this focus increasingly relevant as many traditional algorithms are incapable of fully utilizing such large-scale parallel processing power. We propose a randomized parallel algorithm which computes the fixed point of an arbitrary contraction map on Rbb^n while making full use of large scale computing resources. When the number of processors grows exponentially with n, the proposed algorithm allows for a linear reduction in latency. Though this can also be said of a naive "brute-force" algorithm, the proposed algorithm is characterized by a much better linear factor. A numerical example is used to demonstrate this latency reduction while analytical proofs show this improvement holds in general. We conclude by discussing potential future work in specializing the proposed algorithm for specific applications as well in building a more general theory.

Keywords: Distributed parameter systems, Sliding mode control, Uncertain systems
Abstract: A diffusion equation perturbed by uncertain disturbances of both matching and unmatching nature is considered. The problem of disturbance attenuation is tackled by means of the sliding-mode control approach. It is assumed that only a finite number of pointwise sensing and actuation devices, suitably located in an equi-spaced manner along the spatial domain of interest, is available. We show that an arbitrary level of the unmatching disturbance attenuation can be achieved by employing a sufficiently high number of sensing and actuation devices. We also show that matching disturbances entering the control channels can be fully rejected by the proposed design

Keywords: Distributed parameter systems
Abstract: We consider the problem of boundary stabilization for a system of n coupled parabolic linear PDEs. Particularly, we design a state feedback law with actuation on only one end of the domain and prove exponential stability of the closed loop system with an arbitrarily fast convergence rate. The backstepping method is used for controller design, and the transformation kernel matrix is derived in explicit form by using the method of successive approximations to solve the corresponding PDE. Thus, the suggested control law is also made available in explicit form. Simulation results support the effectiveness of the suggested design.

Keywords: Distributed parameter systems, Distributed control, Networked control systems
Abstract: This paper presents two different design approaches of networked distributed controllers for a class of partial differential equations. Such a work attempts to reduce controller complexity by opting to control a spatially distributed process by a network of interconnected control units. This approach reduces the need to use a centralized controller that must fuse sensory information by the distributed sensors and then dispense the controllers to the spatially distributed process via the spatially distributed actuators. In the first approach, the controller gains used to implement the local controllers by the controller units, along with the actuator and sensor location and the network connectivity are optimized by formulating the optimization problem into a minimization problem of an appropriately chosen performance measure of the closed loop system. This takes the form of a parameterized operator Lyapunov equation whose optimal solution provides the optimal (proportional) controller gains, the optimal locations of the actuators and sensors, and the optimal network connectivity. The second approach considers the adaptation of the gains of the distributed controllers using Lyapunov-redesign methods to extract their adaptation. The well-posedness and convergence properties of the proposed controllers are summarized and numerical studies examining various aspects of the proposed work are presented.

Keywords: Distributed parameter systems, Stability of linear systems
Abstract: This paper considers a boundary control problem of parabolic partial differential equations (PDEs) with an integral of the state variable over the whole spatial domain. To handle this non-strict feedback term, we use a Fredholm-type state transformation that involves two integral terms with kernels defined on the lower and the upper triangular domains. It is shown that the transformation converts the original system with an associated state feedback law into an exponentially stable target system, if the kernels are solutions to a boundary value problem of coupled second-order hyperbolic PDEs. Moreover, the upper kernel is separable if a coefficient of the original system is characterized by a certain parameterized ordinary integro-differential equation. Our approach also provides an explicit feedback gain in a special case. The effectiveness of the proposed controller is confirmed by numerical simulation.

Keywords: Distributed control, Networked control systems, Distributed parameter systems
Abstract: We study spatial homogenization of nonlinear reaction-diffusion PDEs subject to a class of spatially and temporally-varying heterogeneities. We show that an incremental passivity property in the nominal reaction dynamics is fundamental in guaranteeing homogenization of trajectories. Our distributed control achieves homogenization by defining an internal model subsystem for each output corresponding to the respective heterogeneity. We illustrate our algorithm on a system with bistable dynamics. The main contribution of the paper is a constructive approach to guarantee spatial homogenization under heterogeneities.

Keywords: Distributed parameter systems, Networked control systems, Process Control
Abstract: This work presents a methodology for the design and analysis of networked controllers for a class of spatially distributed process systems with uncertain low-order dynamics, discrete sensor-controller communication, and sensor and actuator errors. Initially, a model-based networked controller that enforces exponential closed-loop stability in the absence of sensor and actuator errors is synthesized using an approximate finite-dimensional model of the infinite-dimensional system. Lyapunov techniques are then used to analyze the implementation of the model-based controller in the presence of bounded measurement and actuation errors. Precise conditions for stability and ultimate boundedness of the closed-loop trajectories are derived and used to obtain an explicit characterization of the interdependence between the achievable ultimate bound on the one hand, and the sensor/actuator error bounds, the sensor data transmission rate, the size of process-model mismatch and the choice of sensor/actuator spatial configurations, on the other. It is shown that by judicious selection of these parameters, closed-loop stability with minimal performance degradation can be attained. Finally, the implementation of the networked controller on the infinite-dimensional system is discussed, and the results are illustrated using a diffusion-reaction process example.

Keywords: Networked control systems, Sampled data control, Nonlinear systems
Abstract: We investigate the analysis and design of a control strategy for nonlinear systems under Denial-of-Service attacks. Based on an ISS-Lyapunov function analysis, we provide a characterization of the maximal percentage of time that feedback information can be lost without resulting in instability of the system. Motivated by the presence of a digital channel we consider event-based controllers for which the existence of a minimal inter-sampling time is ensured.

Keywords: Networked control systems, Linear systems
Abstract: We consider a networked control system in which the controller must communicate with the sensors and actuators of the plant through a physical network with fewer communication channels than inputs and outputs. To handle such a system, one typically defines a periodic communication policy specifying which sensors and actuators are connected at any given time. This work considers the situation where the act of switching the physical access to the network takes a finite amount of time, during which no information can be sent. We consider both single-input, single-output and multiple-input, multiple-output, linear, time-invariant plants and determine conditions that guarantee these switching delays to cause the system to lose the properties of reachability and observability.

Keywords: Networked control systems, Model Validation, Communication networks
Abstract: Wireless networked control systems (WNCS) with the control loops closed over a wireless network are prevailing these days. However, due to uncertainties such as random accessing delays and possible packet drops introduced by the wireless communication network, the stability analysis for WNCS is a challenging task. Most previous research on the communication network analysis either simply relied on Monte-Carlo simulation or followed the multi-state Markov chain framework. In this paper, we propose a probabilistic model checking methodology for stability analysis in which the communication system is modelled as a probabilistic timed automaton. The stability condition is written in the probabilistic temporal logic which can be checked and the satisfaction of the specification is equivalent to the stability of the WNCS. With the results from the model checking, we studied the impact of different MAC parameters on the satisfaction of the specification. Furthermore, if the specification is not satisfied initially, we propose a systematic way to design the controller so that the specification can be met. This work presents an attempt and a new angle to the communication and control system co-design problem.

Keywords: Networked control systems, Stability of hybrid systems, Lyapunov methods
Abstract: We design stabilizing controllers for nonlinear networked control systems (NCS) whose transmissions are scheduled by FlexRay. FlexRay protocol has been developed by the automotive industry to provide high bandwidth and deterministic communications. It works with communication cycles which consist of a static segment and a dynamic segment during which different scheduling rules are employed. We generalize existing emulated controller designs to be applicable to NCS with FlexRay. We start from a feedback law which stabilizes the origin of the plant when there is no network. We then present a novel hybrid model of the closed-loop system when the controller is implemented over a network scheduled by FlexRay. Afterwards, we provide conditions on the network under which the stability of the NCS is ensured. In particular, we consider segments of arbitrary lengths and we provide segment-dependent maximal allowable transmission interval bounds. The analysis relies on the construction of a new hybrid Lyapunov function. We believe that this work demonstrates the flexibility of the emulation approach and that it can be used to investigatge other control problems for NCS with switched protocols.

Keywords: Networked control systems, Stability of linear systems, Time varying systems
Abstract: Despite the solid contribution of recent techniques for the analysis of networked controls systems (NCSs), the use of dynamic controllers has received little attention in the literature. Adapting these methods to consider dynamic controllers in the feedback loop is seldom trivial, however, neglecting this class of controllers restricts the universe of applications of these techniques and, consequently, the importance of previous results. In this paper, we establish a new stability criterion suitable for the analysis of NCSs with dynamic controllers. The technique stems from novel Lyapunov-Krasovskii terms and the synthesis of modern techniques for the analysis of time-delay systems adapted to this new scenario. The proposed strategy yields superior results even when particularized for the analysis of NCSs with proportional controllers. Numerical results are provided in order to illustrate the advantages of the proposed criterion and the effectiveness of the theoretical results.

Keywords: Networked control systems, Uncertain systems, Estimation
Abstract: In this work, we consider a state estimation problem for linear uncertain discrete-time systems over a network with dropouts. The uncertainty of the plant model is described by a norm-bounded time-varying parameter that affects the system matrix. We design a jump filter that minimizes an upper bound of the trace of the state estimation error covariance for all possible parameter uncertainties and whose gains are selected from a precalculated finite set depending on the possible measurement reception scenarios. The presented procedure allows us to relate the complexity of the jump filter to the achievable estimation performance.

Keywords: Computer networks, Communication networks, Network analysis and control
Abstract: We study how an underlying network property affects network security when nodes are rational and have four choices -- i) invest in protection, ii) purchase (incomplete coverage) insurance, iii) invest in protection and purchase insurance, or iv) do nothing. More specifically, using a population game model, we examine how the degree distribution of nodes influences their choices at Nash equilibria (NEs) and overall security level. We first show that there exists a degree threshold at NEs so that only the populations with degrees greater than or equal to the threshold invest in protection. Second, as the weighted degree distribution of nodes becomes stochastically larger, the risk or threat posed by a neighbor decreases, even though the aforementioned degree threshold tends to rise, hence only nodes with increasingly higher degrees invest in protection, at the same time. Third, we show that the social optimum also possesses similar properties. Finally, we derive an upper bound on the {em price of anarchy}, which is an affine function of the average degree of nodes. This upper bound is tight in that it is achieved in some scenarios.

Keywords: Computer networks, Distributed control, Lyapunov methods
Abstract: We consider the problem of delivering encoded video to several mobile terminals sharing some limited wireless resource. The aim is to provide some fairness among the terminals in terms of utility, which is cast in the framework of discrete-time linear distributed consensus. To this end, the rate-utility characteristics of each stream is linearized, which allows to get necessary and sufficient conditions on the controller parameters to asymptotically reach the consensus. We also provide a general result on consensus of identical linear systems. Simulation results illustrate the efficiency of the proposed approach and show its robustness to variations of the characteristics of the video streams.

Keywords: Computer networks, Hybrid systems, Stability of hybrid systems
Abstract: We consider the management problem for a cluster of three identical servers treating an external request. We assume that each server has a constant computational speed and we build a deterministic hybrid dynamical model of the overall system. Then, inspired by consensus theory, we propose a centralized control law distributing the computational load among the servers and deciding when to turn on or off each server, for energy efficiency, while ensuring that the queues of each server asymptotically converge to a desirable level. We prove the properties of the proposed law and highlight some interesting peculiarities in terms of non-uniform convergence.

Keywords: Computer networks, Optimization, NL predictive control
Abstract: The widespread diffusion of Infrastructure-as-a-Service and cloud computing paradigms requires large-scale data centers with thousands of running nodes and high energy demands, thus causing relevant economical and environmental costs. In this perspective, the paper presents an energy-aware consolidation strategy based on predictive control, in which virtual machines are migrated among nodes to reduce the number of active units. To describe a general cloud infrastructure, a discrete-time dynamic model is presented together with constraints. The migration strategies of virtual machines are obtained by solving finite-horizon optimal control problems involving integer variables. To reduce the computational effort, approximate solutions are searched for via Monte Carlo optimization. Besides power savings, the proposed method allows one to reduce violations of the service level agreement and aggressive on/off cycles of nodes. To showcase the effectiveness of the proposed approach, preliminary simulation results are provided.

Keywords: Computer networks, Stability of NL systems
Abstract: This paper analyzes previously-proposed dynamic models of content-sharing networks from the point of view of global stability. Our focus is on models that track populations of participating peers as a function of the download progress achieved, described in previous research by a Partial Differential Equation where this progress is a fluid variable. We use such a model to identify conditions on the rate allocation function that make the dynamics preserve a suitable ordering of the state. This enables the application of tools of monotone dynamical systems. This is formally done with finite-dimensional, ordinary differential equation model in which the content fraction index is discrete. Our results apply both to the case of homogeneous upload bandwidths in the participating population, as well as the heterogeneous case with multiple populations of each bandwidth class.

Keywords: Emerging control applications, Computer networks, Queueing systems
Abstract: Cloud applications are often subject to unexpected events like flash crowds and hardware failures. Without a predictable behaviour, users may abandon an unresponsive application. This problem has been partially solved on two separate fronts: first, by adding a self-adaptive feature called brownout inside cloud applications to bound response times by modulating user experience, and, second, by introducing replicas --- copies of the applications having the same functionalities --- for redundancy and adding a load-balancer to direct incoming traffic.

However, existing load-balancing strategies interfere with brownout self adaptivity. Load-balancers are often based on response times, that are already controlled by the self-adaptive features of the application, hence they are not a good indicator of how well a replica is performing.

In this paper, we present novel load-balancing strategies, specifically designed to support brownout applications. They base their decision not on response time, but on user experience degradation. We implemented our strategies in a self-adaptive application simulator, together with some state-of-the-art solutions. Results obtained in multiple scenarios show that the proposed strategies bring significant improvements when compared to the state-of-the-art ones.

Keywords: Autonomous robots, Cooperative control, Maritime control
Abstract: This paper addresses the problem of adaptive leader-follower formation control (ALFC) of autonomous marine vehicles. The rationale for this study can be found in a number of challenging geotechnical surveying missions aimed at mapping geological structures under the seabed. Mission specifications require that a group of surface vehicles equipped with acoustic receivers (hydrophones) maneuver in formation and acquire acoustic data emitted by one or more vehicles that carry acoustic emitters. To this effect, we adopt a basic set-up for ALFC previously proposed for mobile robots modeled as single integrators and extend it to include explicitly the full dynamic equations of a representative type of marine vehicles. The paper offers a formal proof of convergence of the resulting formation control system. Results of simulations illustrate the performance that can be obtained with the control law proposed.

Keywords: Autonomous robots, Kalman filtering
Abstract: The popular extended Kalman filter SLAM (Simultaneous Localization and Mapping) requires the uncertainty is Gaussian noise. This assumption is relaxed to bounded noise by the set membership SLAM. However, the published set membership SLAMs are not suitable for large-scale and on-line problems. In this paper, we use ellipsoid algorithm to SLAM problem. The proposed ellipsoid SLAM has advantages over EKF SLAM and the other set membership SLAM in noise requirement, on-line realization, and large-scale SLAM. By bounded ellipsoid technique, we analyze the convergence and stability of the novel algorithm. Simulation and experimental results are presented that the ellipsoid SLAM is effective for on-line and large-scale problems such as Victoria Park dataset.

Keywords: Autonomous robots, Maritime control, Robust control
Abstract: Three-dimensional curve tracking is an important and challenging research topic for autonomous underwater vehicles and robots. In this paper we consider the tracking control of gliding robotic fish, a new type of energy-efficient and highly maneuverable robots representing a hybrid of underwater gliders and robotic fish; in particular, buoyancy-driven gliding with a deflected tail results in efficient spiral maneuvers. We propose to decompose a space curve into continuously evolving spirals from the viewpoint of differential geometry, and then utilize the spiral trajectory characteristics for three-dimensional curve tracking. Due to the nonlinear dynamics and strong coupling among multiple control inputs, the design of controller is highly demanding. A novel two degree-of-freedom (DOF) tracking control strategy is proposed, which consists of a feedforward inverse controller and a robust H-inf controller designed based on linearized dynamics. Simulation results are presented to demonstrate the effectiveness of the proposed two-DOF control scheme, in comparison with a PI controller and a pure feedforward inverse controller.

Keywords: Autonomous robots, Robotics, Kalman filtering
Abstract: In this work a novel solution to the Simultaneous Localization and Mapping (SLAM) problem for a mobile robot moving in an unknown indoor environment is proposed. The algorithm uses an Extended Kalman filter and a set of polynomials to map the robot surrounding environment boundaries. The main idea behind the proposed SLAM solution is to use the SLAM landmark extraction process to map the environment boundaries shape and the Kalman filter to estimate boundaries position. The algorithm uses measurements taken from a set of distance sensors placed on the robot. The proposed method has been evaluated in both numerical and experimental tests obtaining satisfactory estimation and mapping results.

Keywords: Autonomous robots, Robotics, Stochastic systems
Abstract: We investigate how to improve the autonomy of AUVs to operate effectively in a multistatic network for littoral surveillance. We present a novel algorithm to control the movement of an AUV towing a line array acting as a receiver node in the network. The proposed algorithm uses a non-myopic, receding horizon policy to control the AUV heading to minimize the expected target position estimation error of a tracking filter. Minimizing this error is typically of the utmost interest in target state estimation since it is one way of maintaining track. Methods to simplify the resulting decision tree are used together with a branch and bound technique to solve an optimization problem at each ping time with the low computational power available onboard AUVs. Results from COLLAB13 sea trials are reported and show both the feasibility of running the algorithm in real-time on an onboard computer and the benefits of using the proposed algorithm over conventional predefined paths. These results represent, to the best of our knowledge, the first successful demonstration at sea of a complex non-myopic algorithm running in real-time on AUVs in a realistic multistatic littoral surveillance scenario.

Keywords: Autonomous robots, Robotics
Abstract: Motion planning has been studied for nearly four decades now. Complete, combinatorial motion planning approaches are theoretically well-rooted with completeness guarantees but they are hard to implement. Sampling-based and heuristic methods are easy to implement and quite simple to customize but they lack completeness guarantees. Can the best of both worlds be ever achieved, particularly for mission critical applications such as robotic surgery, space explorations, and handling hazardous material? In this paper, we answer affirmatively to that question. We present a new methodology, NUROA, to numerically approximate the Canny's roadmap, which is a network of one-dimensional algebraic curves. Our algorithm encloses the roadmap with a chain of tiny boxes each of which contains a piece of the roadmap and whose connectivity captures the roadmap connectivity. It starts by enclosing the entire space with a box. In each iteration, remaining boxes are shrunk on all sides and then split into smaller sized boxes. Those boxes that are empty are detected in the shrink phase and removed. The algorithm terminates when all remaining boxes are smaller than a resolution that can be either given as input or automatically computed using root separation lower bounds. Shrink operation is cast as a polynomial optimization with semialgebraic constraints, which is in turn transformed into a (sequence of) semidefinite programs (SDP) using the Lasserre's approach. NUROA's success is due to fast SDP solvers. NUROA correctly captured the connectivity of multiple curves/skeletons whereas competitors such as IBEX and Realpaver failed in some cases. Since boxes are independent from one another, NUROA can be parallelized particularly on GPUs. NUROA is available as an open source package at http://nuroa.sourceforge.net/.

Keywords: Agents and autonomous systems, Adaptive control, Cooperative control
Abstract: Control algorithms of networked multiagent systems are generally computed distributively without having a centralized entity monitoring the activity of agents; and therefore, adverse events such as attacks to the communication network and/or failure of agent-wise components can easily result in system instability and prohibit the accomplishment of system-level objectives. This paper studies resilient coordination of networked multiagent systems in the presence of misbehaving agents, i.e., agents that are subject to such adverse events. In particular, we consider a class of adverse conditions consisting of exogenous disturbances and interagent uncertainties, and present a distributed adaptive control architecture to retrieve the nominal networked multiagent system behavior. Departing from the existing relevant literature that make specific assumptions on the graph topology and/or the fraction of misbehaving agents, we show that the considered class of adverse conditions can be mitigated through a new adaptive control methodology that utilizes a local state emulator -- even if all agents are misbehaving. A illustrative numerical example is provided to demonstrate the theoretical findings.

Keywords: Agents and autonomous systems, Autonomous robots, Cooperative control
Abstract: This study proposes a formal way of representing the dancers in a salsa performance as a transition system. The model involves two finite state machines that communicate through a channel and the goal is to understand the notion of optimality in salsa. This is achieved by integrating two complexity metrics that measure the energy and entropy of the sequences generated by the dancers. These metrics are used as constraints on the transition model for automated dance sequence generation. It is shown that the terms such as `surprising', `unsurprising', `high energy' and `low energy' that are used to describe dance can be formally defined as the constraints on the transition system. In the second part of the study, communication protocols for the construction of distinct dance phrases are investigated. Bounds on the communication complexity are related to the structure of the sequences to be performed by the agents. There is a discussion of results of an experiment in which experienced and beginner level leaders perform dance sequences. The dancers are allowed to make mistakes but asked to continue performing even when a mistake occurs. This scenario is represented by a transition model which involves communication through a multi-input erasure channel. The results of the experiment suggest that a more experienced leader corresponds to having higher channel capacity in transmitting signals to the follower.

Keywords: Agents and autonomous systems, Autonomous robots, Cooperative control
Abstract: In this paper, we investigate set Input to State Stability (set-ISS) in the context of multi-agent systems, specifically when agent interaction is spatial in nature. As a case study we consider an aggregative objective with collision avoidance, where it is assumed that interacting agents are symmetrically disturbed. By considering constraints on physical occupancy in the workspace, we obtain insights into the tradeoffs of disturbance, collective behaviors, and the parameters of interaction. Finally, a feedback loop is generated using the disturbance information yielded by set-ISS analysis to strengthen cohesion against disturbance.

Keywords: Agents and autonomous systems, Autonomous robots, Cooperative control
Abstract: This paper deals with the cooperative source localization problem with the goal of having an accurate estimate of the coordinate of the source cooperatively by a group of unicycle-type mobile agents. Neither absolute positioning information nor a common sense of direction is shared by the agents. Each agent gets its estimate about the source's coordinate in its own local frame based on the bearing measurements about its neighbors (that may or may not include the source) together with its own linear and angular speed information. A continuous time estimation scheme and a distributed fusion scheme are proposed for this goal such that the source's relative coordinate can be estimated at any time by each agent no matter whether it can directly detect the source or not. The globally asymptotic convergence of the estimation scheme and the fusion scheme is rigorously analyzed. Simulation results are also provided to verify the effectiveness of the proposed algorithms.

Keywords: Agents and autonomous systems, Autonomous robots, Networked control systems
Abstract: We consider a generalized Voronoi partitioning problem for a team of vehicles with planar rigid body dynamics. The proximity metric, that is, the generalized metric that determines the proximity relations between the vehicles and arbitrary points in the configuration space, corresponds to the decrease of a generalized energy metric that takes place during the transfer of each vehicle to its goal configuration. In particular, the employed proximity metric is induced by a quasi-Lyapunov function of a corresponding stabilization problem. One of the main motivations for the choice of this proximity metric is to obtain a class of spatial partitions whose computational cost is significantly lower than the one of spatial partitions whose proximity metric is the cost-to-go function of a corresponding optimal control problem, which were studied in our previous work. In particular, the structure of the generalized proximity metric utilized in this work allows us to develop simple and easily implementable partitioning algorithms that are applicable to problems involving vehicles with nonlinear dynamics. More importantly, the proposed partitioning algorithms can be implemented, under some mild assumptions, in a decentralized fashion that allows each vehicle to compute its own cell independently from its teammates. Numerical simulations that illustrate the theoretical developments are also presented.

Keywords: Agents and autonomous systems, Autonomous systems, Robotics
Abstract: We present a simple leader follower tracking controller for autonomous vehicles following straight paths. The difficulty of this problem lies in the fact that the system is not controllable. We show that global tracking may be achieved using controllers having a property of persistency of xcitation, tailored for nonlinear systems. Roughly speaking the stabilization mechanism relies on exciting the system by an amount that is proportional to the tracking error. Then, the method is used to solve the problem of formation tracking of multiple vehicles interconnected on the basis of a spanning-tree topology i.e., each vehicle communicates with one leader and one follower only.

Keywords: Biomolecular systems, Biological systems, Genetic regulatory systems
Abstract: One of the fundamental challenges in implementing complex biocircuits is understanding how the spatial arrangement of biological parts impacts biocircuit behavior. We develop a set of synthetic biology parts for systematically probing the effects of spatial arrangement on levels of transcription. Our initial experimental assays prove that even the rearrangement of two biocircuit parts (comprised of a promoter, coding sequence, and terminator) into three spatially distinct orientations (convergent, divergent, and tandem orientation) can exhibit significantly different levels of transcription. These findings motivate the need for mathematical models to describe these spatial context effects. We pose a novel nonlinear mass-action kinetics based model that enables the integration of knowledge about spatial or compositional context and canonical descriptions of transcriptional dynamics. Our findings suggest that compositional context plays a role in biocircuit part performance and comprise an important piece of biocircuit interconnection theory.

Keywords: Cellular dynamics, Biological systems, Large-scale systems
Abstract: We propose a compartmental lateral inhibition system that generates contrasting patterns of gene expression between neighboring compartments. The system consists of a set of compartments interconnected by channels. Each compartment contains a colony of cells that produce diffusible molecules to be detected by the neighboring colony, and each cell is equipped with an inhibitory circuit that reduces its production when the detected signal is stronger. We develop a technique to analyze the steady-state patterns emerging from this lateral inhibition system and apply it to a specific implementation. The analysis shows that the proposed system indeed exhibits contrasting patterns within realistic parameter ranges.

Keywords: Biomolecular systems
Abstract: Interconnections of biomolecular networks result in new steady states, compared to isolated subsystems, due to the context-dependent effect of perturbations of subsystem "local" parameters like total enzyme availabilities. This paper presents a new theoretical approach, and an algorithm derived from the approach, which allows the determination of the signs of global changes in steady states upon perturbation of parameters in individual subsystems. The algorithm is illustrated through the application to an eukaryotic pathway of central interest in cell signaling.

Keywords: Cellular dynamics, Biomolecular systems, Genetic regulatory systems
Abstract: Bacteria have the ability to sense environmental stress signals and translate them into the appropriate response necessary for survival. One recurring mechanism used for this are two-component systems composed of membrane-bound sensory proteins and response regulator proteins. The regulator proteins are transcription factors that activate a set of genes necessary to trigger the global response leading to phenotypic switching. Measuring the activity of these regulators is essential to the understanding of the stress response and is typically done through the insertion of non-native fluorescent reporter proteins. Introduction of these reporters inside the cell can cause loading as they interfere with the native cell response and regulator activity. In this paper we use mathematical modelling and analysis of a typical response mechanism to show how loading can bias the measurements and cause misidentification of important characteristics of the stress-induced response, such as its qualitative nature and the thresholds that cause phenotypic switching. We establish an approach for determining the presence of loading effects using single cell measurements and biochemical stochasticity of the reporter mechanism. The fluorescence measurements of the loaded system are shown to have different noise characteristics compared to unloaded systems, with larger loads creating more significant differences. The approach depends only on knowing the structural properties of the response model and the load, and it does not rely on the identification of model parameter values.

Keywords: Cellular dynamics, Biomolecular systems, Genetic regulatory systems
Abstract: Gene circuits share transcriptional and translational resources in the cell. The fact that these common resources are available only in limited amounts leads to unexpected couplings in protein expressions. As a result, our predictive ability of describing the behavior of gene circuits is limited. In this paper, we consider the simultaneous expression of proteins and describe the coupling among protein concentrations due to competition for RNA polymerase and ribosomes. In particular, we identify the limitations and trade-offs in gene expression by characterizing the attainable combinations of protein concentrations. We further present two application examples of our results: we show that even in the absence of regulatory linkages, genes can seemingly behave as repressors, and surprisingly, as activators to each other, purely due to the limited availability of shared cellular resources.

Keywords: Cellular dynamics, Genetic regulatory systems, Modeling
Abstract: In this paper we develop a model of gene expression for the purpose of studying the resource use of synthetic gene circuits when expressed in chassis cells. This model focuses on the translational aspect of gene expression which accounts for the majority of resource usage. The model allows for simulations of circuit-chassis interactions that can be used to inform improved designs of synthetic gene circuits.

Keywords: Switched systems, Agents and autonomous systems
Abstract: In this work, we discuss the stability of a discrete-time linear autonomous system under regular switching sequences, whose switching sequences are generated by a Muller automaton. The asymptotic stability of this system, referred to as regular asymptotic stability, generalizes two well-known definitions of stability of autonomous discrete-time linear switched systems, namely absolute asymptotic stability (AAS) and shuffle asymptotic stability (SAS). We also extend these stability definitions to robust versions. We prove that absolute asymptotic stability, robust absolute asymptotic stability and robust shuffle asymptotic stability are equivalent to exponential stability. In addition, by using the Kronecker product, we prove that a robust regular asymptotic stability problem is equivalent to the conjunction of several robust absolute asymptotic stability problems.

Keywords: Discrete event systems, Switched systems, Stability of hybrid systems
Abstract: We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed graph. This allows to express the system dynamics as a time invariant difference inclusion. In turn, a modified version of the forward reachability set mapping is utilized to analyze global exponential stability. The developed framework leads to the establishment of an iterative stability verification algorithm.

Keywords: Switched systems, Stability of hybrid systems, Time varying systems
Abstract: This paper mainly addresses the relationship between attractivity, asymptotic stability, and exponential stability of switched systems with delays and uncertainties under four classes of switching signals: Arbitrary switching signals, periodic switching signals, switching signals with constraints of dwell time and average dwell time. The following results are established: If a homogeneous switched system of degree one is robustly uniformly attractive over some class of switching signals, then it is robustly uniformly exponentially stable (and therefore robustly uniformly asymptotically stable) over the same class of switching signals. Applying the result to switched linear systems with delays and uncertainties, one can check their exponential stability by their asymptotic stability.

Keywords: Switched systems, Linear systems, Stochastic systems
Abstract: This paper proposes novel lower bounds on a quantity called L^p-norm joint spectral radius, or in short, p-radius, of a finite set of matrices. Despite its wide range of applications, (for example, to the stability of switching linear systems and the uniqueness of the equilibrium solutions of switching linear economical models), algorithms for computing the p-radius are only available in a very limited number of particular cases. We propose lower bounds that do not require any special structure on matrices and are formulated as the maximal spectral radius of a matrix family generated by weighting matrices via Kronecker products. We show on numerical examples that the proposed lower bounds can largely improve the existing ones.

Keywords: Switched systems, LMIs, Lyapunov methods
Abstract: In this paper we consider the stabilizability property for discrete-time switched linear systems. Novel conditions, in LMI form, are presented that permit to combine generality with computational affordability. The relations and implications between different conditions, new ones and taken from literature, for stabilizability are analyzed to infer and compare their conservatism and their complexity.

Keywords: Switched systems, Optimal control, Control over communications
Abstract: We analyze a class of suboptimal policies for regulating the state of a switched linear system to zero while minimizing a quadratic cost. Our novel results provide upper and lower bounds on the performance of instances of this class with respect to the optimal policy and other policies of interest. We present a numerical example illustrating the applicability of the results to event-triggered control.

Keywords: Lyapunov methods, Algebraic/geometric methods, LMIs
Abstract: In this paper, we propose a new convex approach to stability analysis of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the polytope into several convex sub-polytopes with a common vertex at the equilibrium. Then, by using Handelman's theorem, we derive a new set of affine feasibility conditions -solvable by linear programming- on each sub-polytope. Any solution to this feasibility problem yields a piecewise polynomial Lyapunov function on the entire polytope. This is the first result which utilizes Handelman's theorem and decomposition to construct piecewise polynomial Lyapunov functions on arbitrary polytopes. In a computational complexity analysis, we show that for large number of states and large degrees of the Lyapunov function, the complexity of the proposed feasibility problem is less than the complexity of certain semi-definite programs associated with alternative methods based on Sum-of-Squares or Polya's theorem. Using different types of convex polytopes, we assess the accuracy of the algorithm in estimating the region of attraction of the equilibrium point of the reverse-time Van Der Pol oscillator.

Keywords: Lyapunov methods, Large-scale systems, Computational methods
Abstract: Dissipativity analysis is an important tool for the analysis of the dynamic response of systems of Ordinary Differential Equations to structural and parametric perturbations. In order to certify dissipativity, semi-definite programming is commonly used for the computation of storage functions of polynomial systems, but is currently not a practical solution for large-scale systems. This paper formulates the computation of a class of structured storage functions that exploit the structure of systems that can be decomposed into cascades. Structured storage functions allow the decomposition of the semi-definite programs used to prove dissipativity, thereby reducing the computational cost of SOS programming and making its application to large-scale systems more practical. Thus structured storage functions deliver additional speed and flexibility to the dissipativity approach to parametric and structural sensitivity analysis.

Keywords: Lyapunov methods, Nonlinear systems, Sliding mode control
Abstract: Finding an explicit Lyapunov function for stability analysis of a given dynamical system entails the nontrivial task of solving a partial differential inequality. Although many methods for finding Lyapunov functions are available, much remains to be done in this regard since there isn’t a universal constructive method for finding simple, explicit Lyapunov functions for dynamical systems with stable equilibria. Homogeneity properties of systems may be used to address this problem since they are capable of reducing the complexity of the equations involved. The present work outlines a method to obtain homogeneous Lyapunov functions for homogeneous second-order systems. In comparison with previous results, the method described here provides explicit Lyapunov functions for a larger set of dynamical systems and greatly reduces the sign-definiteness analysis of the underlying equations.

Keywords: Lyapunov methods, Stability of NL systems, Sliding mode control
Abstract: In this paper a method to design homogeneous Lyapunov functions for a class of homogeneous dynamical systems is proposed. The method is constructive and simple. The procedure exploits homogeneity and polynomial-like properties of the class of functions considered for the vector fields and for the Lyapunov function candidates. It also makes strong use of an algebraic result known as Polya's Theorem to establish the required positive and negative definite properties of the Lyapunov function and its derivative. We illustrate the method by designing smooth Lyapunov functions for two systems. The first one is a Second Order Sliding Mode algorithm known as Super-Twisting. We propose here for the first time a smooth Lyapunov function for it. The second example corresponds to a double integrator controlled by a continuous homogeneous state feedback, whose origin is finite time stable.

Keywords: Nonlinear systems, Lyapunov methods, Computational methods
Abstract: The numerical construction of Lyapunov functions provides useful information on system behavior. In the Continuous and Piecewise Affine (CPA) method, linear programming is used to compute a CPA Lyapunov function for continuous nonlinear systems. This method is relatively slow due to the linear program that has to be solved. A recent proposal was to compute the CPA Lyapunov function based on a Lyapunov function in a converse Lyapunov theorem by Yoshizawa. In this paper we propose computing CPA Lyapunov functions using a Lyapunov function construction in a classic converse Lyapunov theorem by Massera. We provide the theory for such a computation and present several examples to illustrate the utility of this approach.

Keywords: Nonlinear systems, Lyapunov methods, Computational methods
Abstract: In this paper, we present a new approach for computing Lyapunov functions for nonlinear discrete-time systems with an asymptotically stable equilibrium at the origin. The proposed method constructs a continuous piecewise affine (CPA) function on a compact subset of the state space containing the origin, given a suitable triangulation or partition of the compact set and values at the vertices of the triangulation. Here, the vertex values are fixed using a function from a classical converse Lyapunov theorem originally due to Yoshizawa. Several numerical examples are presented to illustrate the proposed approach.

Keywords: Autonomous systems, Sliding mode control
Abstract: In this paper, a sliding mode control algorithm is proposed that allows a single, sensor enabled agent to navigate along the boundary of a contaminated region. The proposed control algorithm only requires knowledge of the local measurement of the scalar field. No gradient information is required for the spatial phenomenon and this distinguishes this work from much of the existing literature. The efficacy of the proposed approach is demonstrated using synthetic volcanic eruption dispersion data made available from a complex Lagrangian model.

Keywords: Estimation, Sliding mode control, Nonlinear systems
Abstract: The paper considers the problems of state estimation, unknown input and measurement noise reconstruction for a class of Lipschitz nonlinear system. By taking the measurement noise vector as an extended state vector, the original system is transformed into an augmented descriptor system. For the descriptor system, the necessary and sufficient condition of the existence of the unknown input observer is discussed first. Second, an adaptive and robust sliding mode observer which can estimate the states and the measurement noise of original system simultaneously is developed. Third, a second-order high gain sliding mode observer is used to exactly estimate the derivative of the system outputs in a finite time. By using the estimates of the states and the output derivatives, a kind of algebraic unknown input reconstruction method is proposed. Finally, a simulation example to a modified single-link flexible joint robot is given to illustrate the effectiveness of the proposed method.

Keywords: Sliding mode control, Lyapunov methods, Nonlinear systems
Abstract: A second order sliding mode control design for a mobile hydraulic system, including bounded model uncertainties and external disturbances, is the subject of study. The proposed algorithm provides a continuous control signal, achieving good performance and chattering attenuation in comparison to other sliding-mode-based techniques. The design includes the formulation of a partial stability problem and we provide the required Lyapunov-function-based analysis. Experimental results are performed over an industrial setup and confirm the effectiveness of the methodology. Moreover, promising results of a comparison with the Super-Twisting and PID controllers are presented.

Keywords: Sliding mode control, Output feedback and Observers, Lyapunov methods
Abstract: In this paper we address the problem of establishing conditions for global asymptotic stability in output feedback sliding-mode control. The proposed methodology introduces a linear term in a first-order sliding-mode controller. This allows to characterize the closed loop with the input-to-state stability property. Also, a Lyapunov-based methodology to find the correct gains for this controller is presented.

Keywords: Sliding mode control, Networked control systems, Uncertain systems
Abstract: This paper addresses the design of a model-based event-triggered strategy based on Sliding Mode Control (SMC), so that the overall proposal can be regarded as a networked control scheme. The objective is to reduce to a minimum the number of transmissions of the plant state over the network, in order to alleviate delays and packet loss induced by data transmission traffic. The key idea consists in using the actual system state or a suitably updated model state within the control law, depending on the magnitude of the sliding variable. More specifically, the model state is used within a boundary layer of the sliding manifold, so that a pseudo-equivalent control can be determined. This latter is continuous, which implies an intrinsic chattering alleviation capability of the proposed strategy. The designed networked scheme is assessed in simulation with satisfactory results.

Keywords: Sliding mode control
Abstract: In this paper we propose a modified, non-switching type reaching law for quasi-sliding mode control of linear discrete time dynamic systems. The reaching law determines the sliding variable rate of change proportional to the negative value of the inverse tangent of this variable. The approach proposed in this work helps satisfy input and state constraints in the controlled system, and at the same time it does not excessively damp the system convergence rate when the sliding variable is small. In the second part of this paper the proposed reaching law is successfully applied to solve the periodic review inventory management problem, with suppliers’ constraints explicitly taken into account.

Keywords: Computational methods, Agents and autonomous systems, Optimal control
Abstract: The problem of computing the minimum time to consensus of multiple identical double-integrator agents is considered. A distributed algorithm for computing the final consensus target state is proposed. Local feedback time optimal control laws are synthesized to drive each agent to the computed final consensus target state. Each agent is assumed to know the states of every other agent. As a part of the algorithm, every possible triplet of agents compute their mutual minimum time to consensus. The maximum value among these triplet minimum times is shown to be the required minimum time to consensus for the entire group. Since the required computation can be performed for each triple separately, it can be distributed evenly among the agents.

Keywords: Computational methods, Control of communications systems, Decentralized control
Abstract: In cellular communication networks, Quality of Service (QoS) is defined as the ratio of (i) the user's signal level to (ii) the system noise plus other agents' signal interference levels, and is commonly used to measure the performance of a mobile user over the network. In this paper, Nash Equilibrium strategies, which minimize a linear combination of the system QoS and the transmitted power in code division multiple access (CDMA) networks, are found via an application of mean field control theory. Computational investigations of the decentralized cellular network optimization (CNO) problem via mean field control are presented for downlink and uplink scenarios with uniform and non-uniform agents among other cases.

Keywords: Computational methods, Distributed control, Nonlinear systems
Abstract: A new semi-smooth Newton (SSN) multigrid algorithm is proposed for solving the discretized first order necessary optimality systems that characterize the optimal solutions of a class of 2D semi-linear parabolic PDE optimal control problems with control constraints. To achieve a second order accurate finite difference discretization, we use a leapfrog scheme (with the second-order backward differentiation formula (BDF2)) in time and a standard 5-point stencil in space. The derived well-structured discretized Jacobian matrices greatly facilitate the development of effective smoother in our multigrid algorithm. Numerical simulations are provided to illustrate the efficiency of the proposed method, which validates the second-order accuracy in solution approximations and the optimal linear complexity in computational time.

Keywords: Computational methods, Linear systems, Network analysis and control
Abstract: We prove that a recently published method to verify strong structural controllability of a pair of structural matrices (sA,sB) can be implemented to run with time complexity linear in n + r + nu, where n and r denote the number of columns of sA and sB, respectively, and nu the number of non-zero entries of (sA,sB). Linear complexity is achieved by using sophisticated data structures and sparse matrix techniques. The linear run time of the algorithm is also experimentally demonstrated by computations on matrices of different sparsity and size.

Keywords: LMIs, Optimal control, Optimization
Abstract: In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very broad as a reliable solution to the problem would provide a powerful modeling tool in many areas of experimental science. We propose to use the Hamilton-Jacobi-Bellman sufficient optimality conditions for the direct problem as a tool for analyzing the inverse problem and propose a general method that attempts at solving it numerically with techniques of polynomial optimization and linear matrix inequalities. The relevance of the method is illustrated based on simulations on academic examples under various settings.

Keywords: Computational methods, Nonlinear systems, Linear systems
Abstract: The Adomian decomposition method and the Laplace transformation are employed to analyze approximate closed form solutions of nonlinear oscillatory systems as well as a hyperbolic system, investigating their response to various initial conditions and damping coefficients.

Keywords: Algebraic/geometric methods, Randomized algorithms, Sensor networks
Abstract: In the context of sensor networks, gossip algorithms are a popular, well established technique for achieving consensus when sensor data is encoded in Euclidean spaces. The algorithm also has several extensions to nonlinear data spaces. Most of these extensions deal with Riemannian data spaces and use gradient descent techniques to derive a generalization of the gossip algorithm. However, their heavy reliance on calculus tools hides the simple metric properties that make gossip algorithms work. This paper studies the pairwise gossip algorithm from a purely metric perspective. Focusing on the essential propriety that makes pairwise midpoint gossip converge on Riemannian manifolds, this paper argues that the notion of CAT(0) space is perfectly suited to the analysis of gossip algorithms. The transition from a Riemannian to a purely metrical framework has three virtues: it simplifies the proofs, provably preserves convergence speed of pairwise gossip, yet in a more general framework, and paves the way for new applications, as illustrated by our numerical experiments on robots arms viewed as points in the metric graph associated with the free group

Keywords: Algebraic/geometric methods, Aerospace, Filtering
Abstract: The recently introduced Invariant Extended Kalman Filter (IEKF) is an extended Kalman filter designed for systems admitting symmetries, that possesses interesting convergence properties, and a relative independence of the filter behavior with respect to the system's trajectory. In the present paper, the ideas are extended to a broad class of systems introducing the notion of ``conditional invariance", that is, invariance properties of the system once some of the state variables are known. We exploit this structure by devising an Invariant Rao-Blackwellized Particle Filter: those state variables are sampled, and the rest are marginalized out using IEKFs. The striking property of the obtained particle filter is that the Kalman gains are identical for all particles, leading to a drastic reduction of the computational burden. The strong potential of the method is illustrated by the challenging and realistic problem of localization from noisy inertial sensors and a noisy GPS having a randomly jumping bias.

Keywords: Algebraic/geometric methods, Robust control, Nonlinear systems
Abstract: This paper extends the powerful and intuitive framework of PID control to fully actuated, left-invariant, mechanical systems on a general Lie group. The class of problems solved includes tracking of a smoothly time-varying desired orientation for a rigid body with fully actuated attitude dynamics in two or three dimensions. If the reference velocity and unmodeled disturbance forces converge to constant values, then the closed-loop system will be almost-globally exponentially stable. The controller is robust to errors or variations in the inertial parameters and the actuator parameters. We explicitly construct the controller on the group of rigid body rotations and demonstrate its performance in quadrotor attitude tracking.

Keywords: Algebraic/geometric methods, Stability of NL systems, Emerging control theory
Abstract: The classical third-order model describing the rotation of a rigid body in 3D is here considered, with two torques being applied as controls around two of the three main rotation inertial axes. By using a new method, that we call 'Quadratic Immersion', we show that the global stabilization can be attained with a static state-feedback -- i.e. a static loop making the zero a 'practical' globally asymptotically stable point for the closed-loop system. Here 'practical' adds up to a slight modification of the usual notion of asymptotic stability, where the point is required to lie in just the closure of the closed-loop system domain -- and in particular not to be an equilibrium of the closed-loop system -- and the attraction set is given by re^3 unless a zero-measure set ('almost global'-stability). Such stabilization is exponential, with rate and max overlength that can be arbitrarily and simultaneously set in advance by the designer. Numerical simulations of the method are reported, showing the exponential-stabilizing behavior of the closed loop system in various situations.

Keywords: Algebraic/geometric methods
Abstract: Using a suitable locally convex topology for the space of real analytic vector fields, we give a characterization of real analytic control systems. Among other things, this class of real analytic control systems has the property that, upon substitution of an open-loop control, the resulting time-varying vector field has a flow depending on initial condition in a real analytic manner. To give context to the real analytic case, we also consider the cases of finitely differentiable and smooth control systems.

Keywords: Feedback linearization, Algebraic/geometric methods, Nonlinear systems
Abstract: It is well known that given a controllable system, addition of new actuators cannot make the system to loose the controllability property. For linear systems, since controllability is equivalent to differential flatness, the latter property cannot be lost by addition of new inputs. However, this is not true for nonlinear systems. In this paper, we investigate under which conditions systems that are perturbed by addition of new inputs retain the property of being linearizable by static feedback linearization. Some sufficient conditions and a necessary one are given. The theory is illustrated with some examples

Keywords: Energy systems, Decentralized control, Stochastic optimal control
Abstract: We study a power system with one independent system operator (ISO) who procures energy from energy generators, and decentralized aggregators who purchase energy from the ISO to serve their customers. With the penetration of renewable energy generation, the aggregators are adopting energy storage to deal with the high volatility in supply and prices. In the presence of energy storage, it is beneficial for all the entities (i.e. the ISO and aggregators) to make foresighted decisions (i.e. energy procurement decisions by the ISO and energy purchase decisions by the aggregators) to minimize their long-term costs. However, the optimal foresighted decision making is complicated mainly because the information required to make optimal decisions is decentralized among the entities. We propose a design framework in which the ISO provides each aggregator with a conjectured future price, and each aggregator distributively minimizes its own long-term cost based on its conjectured price as well as its local information. The proposed framework can achieve the social optimum despite the decentralized information among the entities. Simulation results demonstrate significant reduction in the total cost by the proposed foresighted energy purchase and procurement (EPP), compared to the optimal myopic EPP (up to 60% reduction), and the foresighted EPP based on the Lyapunov optimization framework (up to 30% reduction).

Keywords: Energy systems, Linear parameter-varying systems, H infinity control
Abstract: In this paper a multi-variable LPV/Hinf control approach is applied to design a strategy for power source coordination within a multi-source energy system. Three different kinds of power sources – fuel cell, battery and ultracapacitor – compose the power supply system of an electric vehicle. All sources are current-controlled and paralleled together with their associated DC-DC converters on a common DC-link coupled to vehicle’s electrical motor and its converter. DC-link voltage must be regulated in spite of load power variations representing the driving cycle image. To this end, a MIMO LPV/Hinf provides the three current references so that each source operates in its most suitable frequency range as either high-energy-density or high-power-density source: low-frequency, the mean power is provided by the fuel cell, the ultracapacitor supplies/absorbs the instantaneous variations of power demand and the battery operates in between the two other sources. Selection of Hinf weighting functions is guided by a genetic algorithm whose optimization criterion expresses the frequency-separation requirements. The nonlinear multi-source system is simulated in MATLAB/Simulink using the driving cycle of IFSTTAR (Institut Français des Sciences et Technologies des Transports, de l’Aménagement et des Réseaux) as load profile, whose frequency content is richer than the one of Normalized European Driving Cycle (NEDC). Simulation results show good performance in supplying the load at constant DC-link voltage according to user-configured frequency-separation power sharing strategy.

Keywords: Energy systems, Optimization algorithms, Distributed control
Abstract: We consider the problem of minimizing the power generation cost by exploiting the distributed renewable energy sources (DRES) located in the power distribution network. The proposed strategy requires that the intelligent agents, located at the microgenerator buses, measure their voltage and then adjust the amount of injected power, according to a feedback control law that is indeed a projected gradient descent strategy. Simulations are provided in order to illustrate the algorithm behavior.

Keywords: Energy systems, Optimization algorithms
Abstract: The paper focuses on the scheduling of energy activities in smart homes equipped with controllable electrical appliances, renewable energy sources, dispatchable energy generators, and energy storage systems. We formulate a mixed integer quadratic programming energy scheduling algorithm for cost minimization under nonlinear pricing. The scheduling technique manages the use of electrical appliances, plans the energy production and supplying, and programs the storage systems charging/discharging. A case study simulated in different scenarios demonstrates that the approach allows full exploitation of the potential of local energy generation and storage to reduce the individual user energy consumption costs, while complying with the customer energy needs.

Keywords: Energy systems, Power electronics, Lyapunov methods
Abstract: In order to address the output current imbalanced problem of a parallel charging system with directed communication for energy storage type light rail vehicles, a cooperative current-sharing scheme is proposed in this paper. This parallel charging system is a non-identical nonlinear multi-agent systems with bounded input constraints by considering each charger as an agent. Each charger transmits the current state information to its neighbors via communication network, which can be modeled by a directed graph. Input-output feedback linearization is introduced to convert the current-sharing control of non-identical nonlinear parallel charging system into a first-order multi-rate integrator current consensus-tracking problem. To satisfy the boundedness of control input, a general saturation function is put forward to design the bounded cooperative current-sharing control law based on the nearest neighborhood rule. A novel Lyapunov candidate function depending on the communication topology is proposed to rigorously prove the cooperative current-sharing stability of closed-loop system, which is under the fixed directed topology provided that the digraph only has a directed spanning tree. Several charging schemes are compared and analyzed. The output current of parallel chargers can be balanced by adopting the proposed approach, which is verified by simulating a parallel charging test system.

Keywords: Energy systems, Robust control, Distributed parameter systems
Abstract: A key property that has a close relationship to both the performance and stability of the plasma in nuclear fusion tokamak devices is the safety factor profile (q-profile). As a result, extensive research has been conducted to develop algorithms to actively control the q-profile evolution with the goal of optimizing the tokamak approach to fusion energy production. The actuators that can be used to control the q-profile are the total plasma current, the auxiliary heating/current-drive system and the line-average electron density. In this work, we first investigate the effect that pure plasma auxiliary heating has on the q-profile in low performance (L-mode) operating scenarios in the TCV tokamak. This study indicates that pure auxiliary heating has a small effect on the q-profile in the examined scenarios. Therefore, feedback controllers that utilize the total plasma current and exclusively the auxiliary current-drive capabilities are designed for q-profile control in TCV. The controllers are designed to put emphasis on achieving the target q-profile in different spatial regions and to respond differently to errors in the q-profile. The control performance of each controller is tested with the simplified physics-based plasma profile simulation code RAPTOR. The comparison of the closed-loop performance of these controllers is done in preparation for future q-profile control experiments in the TCV tokamak.

Keywords: Emerging control applications, Automotive control, Autonomous systems
Abstract: Improvements in sensor technology and data processing rates are leading to the collection of vast databases of time series data. These data sets are spawning new applications that are transforming the way we live, work, and learn. In particular in the domain of vehicles, the rapid expansion of sensors to monitor both the state of the system and the occupants has led to an increase in the available data, but the research is still inconclusive on how to best handle this data.

This paper develops one data representation that is scalable in dimension and efficiently stores/retrieves multi-attribute time series in the presence of noise. Here the proposed data representation is a multi-input multi-output autoregressive model (MIMO ARX) with an exogenous input. MIMO ARX models are an advantageous data representation because they are a dimension-reducing representation that inherently describes the inter-dependencies in the data while enabling the creation of efficient noise mitigation approaches. Tests using real-life vehicle data show the effectiveness of these data representations in the application of passenger vehicle localization.

Keywords: Emerging control applications, Optimization, Stochastic optimal control
Abstract: This paper addresses the problem of improving energy efficiency and quality-of-service (QoS) of data centers, by coordinating the “feed-forward” capacity provisioning controller and the “feed-back” load balancing controller. A data center is modeled as a collection of modular server blocks which cooperatively process multi-class, inter-dependent workload. We propose a coordinated two-stage control strategy of data centers based on the adaptive robust optimization framework. In stage 1, the optimal capacity of each server block is found based on predicted arrival rates of future workload, taking into account the potential QoS cost in stage 2; Then in stage 2, the load balancer distributes incoming workload to server blocks to achieve optimal QoS, after observing the actual workload. We show through simulations that the proposed approach achieves lower total costs as well as less QoS variations compared to a start-of-art baseline approach with reasonable level of conservativeness.

Keywords: Emerging control applications, Decentralized control, Networked control systems
Abstract: We present results from a week-long experimental evaluation of a scalable control algorithm for a commercial building heating, ventilation, and air-conditioning (HVAC) system. The experiments showed that the controller resulted in 37% energy savings without sacrificing indoor climate. In contrast to prior work that reports energy savings without a careful measure of the effect on indoor climate, we verify that the controller achieves the energy efficiency improvements without any adverse effect on the indoor climate compared to the building’s baseline controller. This is established from measurements of a host of environmental variables and analysis of before-after occupant survey results. We present a complete system to retrofit existing buildings including the control algorithm and the supporting execution platform which includes the deployment of a wireless sensor network. Results show that there is a large variation in energy savings from zone to zone, which indicates that estimating energy savings potential of novel HVAC control systems is not trivial even from experiments—something that prior work with uniformly positive messages did not emphasize.

Keywords: Emerging control applications, Energy systems
Abstract: The retraction phase of a ground-based airborne wind energy system is the second part of a two phase power generation cycle. In the first phase, energy is produced by exploiting the aerodynamic lift exerted by a wing tethered to the ground and controlled to fly crosswind paths. Power is produced by unreeling the tether, wound around drums connected to generators, under high traction force. In the retraction phase, the tether is reeled-in after its maximum length has been reached. In this paper, a new dynamical model of a tethered wing for the retraction phase is derived from first principles, and a flight controller based on this model, which is straightforward to implement and tune, is proposed. Simulation results comparing this new strategy to an existing approach are presented. Besides a better performance, the main advantage of the new approach is that it uses readily available measurements for feedback control, hence resulting in a more robust and reliable solution.

Keywords: Maritime control
Abstract: A factorized Nonlinear Generalized Minimum Variance (NGMV) control law is developed for a combined roll and yaw motion compensation using rudders and fins. The nonlinear model used for control design includes the non-minimum phase interaction from rudder to roll motion, and the dynamics from fins to yaw motion. This controller is developed using the polynomial approach to ensure that the non-minimum phase system remains stable in closed-loop. The effectiveness of the approach is demonstrated on a simulated nonlinear ship model.

Keywords: Mechatronics
Abstract: The aim of this article is to establish an induced frame vibration and attenuation scheme, specifically targeting the area of multi-rotor Unmanned Aerial Vehicles (UAVs), such as quadrotors. These types of unmanned small scale helicopters are characterized by small and light frames, which are vulnerable to vibrations induced by the operation of the motors or external environmental factors. The existence of such vibrations effecting the frame can significantly deteriorate the performance of the overall closed system and even drive it to instabilities. In this article spectral estimation schemes based on: a) Autoregressive (AR) modeling and b) Multiple Signal Classification (MUSIC) are being established and evaluated towards their ability to detect the induced vibration frequencies on the UAV, while an extended discussion is being presented on selecting the correct number of the identified induced vibrating frequencies. In a sequential stage, a vibration attenuation approach based on notch filtering is being presented, being able to correctly attenuate the induced vibrating frequencies in the measurements. The efficiency of the overall suggested scheme is being evaluated by experimental results that indicate the significant improvement in the measurements achieved by the direct application of the proposed scheme.

Keywords: Biological systems, Statistical learning, System identification
Abstract: This study is primarily motivated by biological applications and focuses on the identification of Boolean networks from scarce and noisy data. We consider two Bayesian experimental design scenarios: selection of the observations under a budget, and input design. The design goal is the maximization of the mutual information between models and data, that is the ultimate statistical upper bound on the identifiability of a system from empirical data. First, we introduce a method to select which components of the state variable to measure under a budget constraint, and at which time points. Our greedy approach takes advantage of the submodularity of the mutual information, and hence requires only a polynomial number of evaluations of the objective to achieve near-optimal design solutions. Second, we consider the computationally harder task of designing sequences of input interventions, and propose a likelihood-free approximation method. Exact and approximate design solutions are verified with predictive models of genetic regulatory interaction networks in embryonic development.

Keywords: Optimization algorithms, Statistical learning, Computational methods
Abstract: Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering. Computing the least squares (LS) estimator via solving a quadratic program (QP) is the most common technique to fit a piecewise-linear convex function to the observed data. Since the number of constraints in the QP formulation increases quadratically in N, the number of observed data points, computing the LS estimator is not practical using interior point methods when N is very large. The first-order method proposed in this paper carefully manages the memory usage through parallelization, and efficiently solves large-scale instances of CR.

Keywords: Statistical learning, Adaptive control, Autonomous systems
Abstract: We propose a satisficing objective for the multi-armed bandit problem, i.e., where the objective is to achieve performance above a given threshold. We show that this new problem is equivalent to a standard multi-armed bandit problem with a maximizing objective and use this equivalence to find bounds on performance in terms of the satisficing objective. For the special case of Gaussian rewards we show that the satisficing problem is equivalent to a related standard multi-armed bandit problem again with Gaussian rewards. We apply the Upper Credible Limit (UCL) algorithm to this standard problem and show how it achieves optimal performance in terms of the satisficing objective.

Keywords: Statistical learning, Estimation, Agents and autonomous systems
Abstract: The spread of contaminant into the environment due to a high volume of leakage from point sources is a very real threat in the modern world. Since the contaminant can often be dangerous to human operators, multiple robotic agents equipped with suitable sensors are playing an increasingly important role in the so-called contaminant detection problem than before. This paper proposes a contaminant detection methodology which can not only locate the (possibly multiple) source of the contaminant, but also estimate the intensity in an environment evolving over both space and time. The method can deal with measurement noise and does not need any gradient information.

Keywords: Statistical learning, Estimation, Network analysis and control
Abstract: This work is concerned with the problem of social learning. A network of agents attempt to learn some unknown state of the world which is drawn by nature from a finite set. The sources of information available to the agents are their own private observations as well as the beliefs of their neighboring agents in the social structure in which they interact. The rational approach to the problem of social learning is for each agent to refine her opinion, by using the Bayes' rule to incorporate her neighbors' beliefs and own private signals over time. However, repeated applications of the Bayes' rule in social networks can become computationally intractable, partly due to the fact that each agent needs to use her local data that is increasing over time and make inferences about the global network structure. The inherent complexity of the Bayesian approach has lead to the consideration of behavioral, non-Bayesian updates, where each agent instead of processing all new information in the optimum Bayesian way uses simple rules such as linear or convex combinations and forms updated beliefs. In this paper, it is shown that by replicating the rule that maps the agents' common prior to their Bayesian posterior at the initial time-step for all future steps, one can derive a memoryless Bayesian update that has a log-linear format and can serve as a theoretical justification for some of the non-Bayesian rules suggested in the literature. Convergence and learning under the derived rules are also investigated, and it is shown that while two communicating agents always learn the true state, the beliefs may fail to converge in the general network setting. The proposed approach has the advantage that while preserving some features of the Bayesian inference, they are made tractable.

Keywords: Statistical learning, Optimization, Computational methods
Abstract: We study the problem of estimating sparse precision matrices from data with missing values. We show that the corresponding maximum likelihood problem is a Difference of Convex (DC) program by proving some new concavity results on the Schur complements. We propose a new algorithm to solve this problem based on the ConCave-Convex Procedure (CCCP), and we show that the standard EM procedure is a weaker CCCP for this problem. Numerical experiments show that our new algorithm, called m-CCCP, converges much faster than EM in number of iterations on both synthetic and biology datasets.

Keywords: Fault detection, Switched systems, Markov processes
Abstract: In this paper, the problem of integrated fault detection, isolation and control (IFDIC) design of continuous-time Markovian jump linear systems with uncertain transition probabilities is presented. A single Markovian jump module designated as IFDIC under a mixed H∞/H− framework is considered and designed in order to simultaneously achieve the desired detection, isolation and control objectives. The conventional mixed H∞/H− approach leads to conservative results due to the selection of identical Lyapunov matrices. Consequently, extended linear matrix inequalities (LMIs) methods are used in this work to reduce the conservativeness by introduction of additional matrix variables so that the couplings of the Lyapunov matrices with the system matrices are eliminated. Simulation results for the GE F-404 aircraft engine system illustrate the effectiveness of our proposed design methodologies. Comparisons with relevant work in the literature are also provided to demonstrate the utility of our proposed solutions.

Keywords: Fault diagnosis, Variational methods, Linear system observers
Abstract: In this paper, a previously published discrete-time game theoretic fault detection filter is generalized to the multiple-fault case. The derivation models the detection filter problem as a collection of disturbance attenuation problems, which are optimized via a single cost function. Once solved, the implied discrete-time Riccati inequalities may be used as the constraints of a secondary cost function, which is optimized to find a specific filter gain that achieves secondary objectives. Furthermore, it is shown that the novel detection filter approximates those obtained using spectral and geometric theories, improves their robustness to noise and initial condition errors, and models sensor faults directly rather than requiring that they be rewritten as dynamic faults.

Keywords: Fault diagnosis, Distributed parameter systems, Fault detection
Abstract: This paper addresses a new model-based fault diagnostics and prognostics scheme for distributed parameter systems described by a class of partial differential equations (PDEs). Under the assumption that system state is available, an observer is proposed based on the PDE representation and a fault is detected by comparing the detection residual, which is defined as the difference between the output of the observer and the physical system, to a predefined threshold. Subsequently, the fault function is estimated and its parameters are tuned by a novel update law using system state information. The parameter magnitudes and the tuning law are utilized to determine the time to failure (TTF). In order to relax the need for state availability, two output filters and one input filter are introduced. Finally, the performance of the state and filter based diagnostics and prognostics scheme is evaluated by using a heat transfer reactor with an actuator fault.

Keywords: Fault detection, Fault diagnosis, Uncertain systems
Abstract: A number of residual generation methods have been developed for robust model-based fault detection and isolation (FDI). There have also been a number of offline (i.e., design-time) methods that focus on optimizing FDI performance (e.g., trading off detection performance versus cost). However, design-time algorithms are not tuned to optimize performance for different operating regions of system behavior. To do this, would need to define online measures of sensitivity and robustness, and use them to select the best residual set online as system behavior transitions between operating regions. In this paper we develop a quantitative measure of residual performance, called the detectability ratio that applies to additive and multiplicative uncertainties when determining the best residual set in different operating regions. We discuss this methodology and demonstrate its effectiveness using a case study.

Keywords: Fault detection, Machine learning
Abstract: In this paper, the use of the Principal Direction Divisive Partitioning (PDDP) method for unsupervised learning is discussed and analyzed with a focus on fault detection applications. Specifically, a geometric limit of the standard algorithm is highlighted by means of a simulation example and a modified version of PDDP is introduced. Such a method is shown to correcly perform data clustering also when the standard algorithm fails. The modified strategy is based on the use of a Chi-squared statistical test and offers more guarantees in terms of detection of a wrong functioning of the system. The proposed algorithm is finally experimentally tested on a fault detection application for aerospace electro-mechanical actuators, for which a comparison with k-means and fuzzy k-means approaches is also provided.

Keywords: Fault detection, Emerging control applications, Communication networks
Abstract: This paper considers a method of coding the sensor outputs in order to detect stealthy false data injection attacks. An intelligent attacker can design a sequence of data injection to sensors that pass the state estimator and statistical fault detector, based on knowledge of the system parameters. To stay undetected, the injected data should increase the state estimation errors while keep the estimation residues in a small range. We employ a coding matrix to the original sensor outputs to increase the estimation residues, such that the alarm will be triggered by the detector even under intelligent data injection attacks. This is a low cost method compared with encryption over sensor communication networks. We prove the conditions the coding matrix should satisfy under the assumption that the attacker does not know the coding matrix yet. An iterative optimization algorithm is developed to compute a feasible coding matrix, and, we show that in general, multiple feasible coding matrices exist.

Keywords: Estimation, Quantum information and control, Linear systems
Abstract: We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a variable for the quantum plant. We demonstrate that for a passive plant that can be characterized by annihilation operators only, such coherent-classical estimation provides no improvement over purely-classical estimation. An example is also given which shows that if the plant is not assumed to be an annihilation operator only quantum system, it is possible to get better estimates with such coherent-classical estimation compared with purely-classical estimation.

Keywords: Optimal control, Nonlinear systems, Quantum information and control
Abstract: The contrast problem in nuclear magnetic resonance imaging has been treated by a variety of recent works. In this process, the image is typically captured multiple times to filter noise from the image, and to do so the system must return to its initial state before repeating the experiment. A natural motivation is to perform this return trip as quickly as possible, in particular with live subjects.

In this article we introduce and discuss preliminary results this so-called return trip of the contrast problem. The tools of geometric optimal control theory have been effectively applied to the contrast problem, and they are similarly employed to this problem which shares many characteristics. The time-minimal transfer in the single-spin case is presented, and preliminary results in the two-spin case are given.

Keywords: Quantum information and control, Algebraic/geometric methods, Nonlinear systems
Abstract: Quantum coherence of open quantum systems is usually compromised because of the interaction with the ambient environment. Here, we introduce the concept of Decoherence Splitting Manifold (DSM), a submanifold of the space of density operators, wherein the system's density matrix clearly exhibits a splitting between a unitarily evolving sub-density corresponding to some given set of its eigenvalues, which we aim to preserve, and another subdensity, in which eigenvalues are not preserved. The eigenspace of the eigenvalues that are preserved provides the concept of (time-varying) Decoherence Protected Subspace (DPS), a concept that subtlety differs from the (time-varying) Decoherence Free Subspace (DFS) in the way the protected subspace is embedded in the full Hilbert space. With the DSM concept, the DPS is reformulated as a complex vector bundle over the DSM. In the absence of the traditional DFS, looking for less restrictive spaces and/or utilizing quantum control may help generate and/or retain a decoherence-free subevolution. This is achieved by searching for a DSM whose tangent bundle distribution is invariant under indirect control of an auxiliary qubit.

Keywords: Quantum information and control, Uncertain systems, Sampled data control
Abstract: In this paper, a sampling-based learning control (SLC) algorithm is used to find a robust control law that can steer a quantum system with uncertainties into a maximally entangled state. The quantum system under consideration consists of two two-level atoms interacting with a quantized electromagnetic field. In the sampling-based learning control method, an artificial system is constructed based on the quantum system with uncertainties and an optimal control law is learned for the artificial system. Some additional samples which are generated by sampling the uncertainty parameters are used to test the performance of the optimal control law. Numerical results demonstrate the effectiveness of the SLC method in finding a robust control law for entanglement generation between two atoms in a cavity in the presence of a quantized field.

Keywords: Quantum information and control
Abstract: This paper presents a novel characterization of completely passive linear quantum stochastic systems solely in terms of the controllability Gramian of such systems. Importantly, exploiting this result, we establish a connection between the class of completely passive systems and the class of linear quantum stochastic systems with a pure Gaussian steady state. Consequently, we obtain a new complete parameterization for the class of systems generating a pure Gaussian steady state. Examples are provided to illustrate our results.

Keywords: Quantum information and control
Abstract: Recent work has shown that deploying two nondegenerate optical parametric amplifiers (NOPAs) separately at two distant parties in a coherent feedback loop generates stronger Einstein-Podolski-Rosen (EPR) entanglement between two propagating continuous-mode output fields than a single NOPA under same pump power, decay rate and transmission losses. This paper aims to investigate the stability and EPR entanglement of a dual-NOPA coherent feedback system under the effect of phase shifts in the transmission channel between two distant parties. It is shown that, in the presence of phase shifts, EPR entanglement worsens or can vanish, but can be improved to some extent in certain scenarios by adding a phase shifter at each output with a certain value of phase shift.

Keywords: Optimization algorithms, Predictive control for linear systems, Optimal control
Abstract: We investigate the infeasibility detection in the alternating direction method of multipliers (ADMM) when minimizing a convex quadratic objective subject to linear equalities and simple bounds. The ADMM formulation consists of alternating between an equality constrained quadratic program (QP) and a projection onto the bounds. We show that: (i) the sequence of iterates generated by ADMM diverges, (ii) the divergence is restricted to the component of the multipliers along the range space of the constraints and (iii) the primal iterates converge to a minimizer of the Euclidean distance between the subspace defined by equality constraints and the convex set defined by bounds. In addition, we derive the optimal value for the step size parameter in the ADMM algorithm that maximizes the rate of convergence of the primal iterates and dual iterates along the null space. In fact, the optimal step size parameter for the infeasible instances is identical to that for the feasible instances. The theoretical results allow us to specify a practical termination condition for infeasibility and the performance of such criterion is demonstrated in a model predictive control application.

Keywords: Optimization algorithms, Algebraic/geometric methods, Biomolecular systems
Abstract: In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.

Keywords: Variational methods, Optimization algorithms, Game theory
Abstract: We consider stochastic variational inequality problems where the mapping is monotone over a compact convex set. We present two robust variants of stochastic extragradient algorithms for solving such problems. Of these, the first scheme employs an iterative averaging technique where we consider a generalized choice for the weights in the averaged sequence. Our first contribution is to show that using an appropriate choice for these weights, a suitably defined gap function attains the optimal rate of convergence. In the second part of the paper, under an additional assumption of weak-sharpness, we update the stepsize sequence using a recursive rule that leverages problem parameters. The second contribution lies in showing that employing such a sequence, the extragradient algorithm possesses almost-sure convergence to the solution as well as convergence in a mean-squared sense to the solution of the problem at the rate of O(1/k). Motivated by the absence of a Lipschitzian parameter, in both schemes we utilize a locally randomized smoothing scheme. Importantly, by approximating a smooth mapping, this scheme enables us to estimate the Lipschitzian parameter. The smoothing parameter is updated per iteration and we show convergence to the solution of the original problem in both algorithms.

Keywords: Optimization algorithms, Sliding mode control, Energy systems
Abstract: The aim of this paper is to present a new dynamical system which solves linear programming. Its design is considered as a sliding mode control problem, where its structure is based on the Karush-Kuhn-Tucker optimality conditions, and its multipliers are the control inputs to be implemented by using fixed time stabilizing terms with vectorial structure, based on the unit control, instead of common terms used in other approaches. Thus, the main features of the proposed system are the fixed convergence time to the programming solution and the fixed parameters number despite of the optimization problem dimension. That is, there is a time independent to the initial conditions in which the system converges to the solution and, the proposed structure can be easily scaled from a small to a higher dimension problem. The applicability of the proposed scheme is tested on real-time optimization of an electrical Microgrid prototype.

Keywords: Optimization algorithms, Distributed control, Computational methods
Abstract: This paper considers the problem of solving Quadratic Programs (QP) arising in the context of distributed optimization and optimal control. A dual decomposition approach is used, where the problem is decomposed and solved in parallel, while the coupling constraints are enforced via manipulating the dual variables. In this paper, the local problems are solved using a primal-dual interior point method and the dual variables are updated using a Newton iteration, providing a fast convergence rate. Linear predictors for the local primaldual variables and the dual variables are introduced to help the convergence of the algorithm. We observe a fast and consistent practical convergence for the proposed algorithm.

Keywords: Optimization algorithms, Optimization
Abstract: In this paper, a Riemannian conjugate gradient method for a Riemannian optimization problem related to the singular value decomposition of a complex matrix is developed. The proposed algorithm is globally convergent, unlike Newton's method. However, Newton's method for this problem is locally quadratically convergent. With this in mind, the proposed conjugate gradient method is combined with Newton's method to produce a hybrid algorithm, which is globally and quadratically convergent in practice.

Keywords: Optimal control, Algebraic/geometric methods
Abstract: We consider an optimal control problem defined on a Lie group whose associated Hamiltonian function is left-invariant under the action of a subgroup of the Lie group. Necessary conditions for optimality are derived using Lie-Poisson reduction for semidirect products, which allows us to study the Hamiltonian system in a space of lower dimension. Our main contribution is a reduced sufficient condition for optimality that relies on the nonexistence of conjugate points. We derive coordinate formulae for computing conjugate points in the reduced Hamiltonian system, and we relate these conjugate points to local optimality in the original optimal control problem. These conditions are applied to an optimal control problem that can be used to model either a kinematic airplane or a Kirchhoff elastic rod in a gravitational field.

Keywords: Optimal control, Biological systems, Nonlinear systems
Abstract: This paper presents a method for finding the optimal turning gait of a robotic locomotor, which rectifies periodic motion of the mechanical body into sustained propulsive force through interactions with the environment. First, equations of motion for a general rectifier traveling in three dimensional space are developed in body coordinates, and accelerations are shown to be independent of body orientation. A simplified model is then developed to capture the essential dynamics, assuming small body deformation. An optimal gait problem is formulated for the simplified model as the minimization of a quadratic cost function, subject to constraints on average nominal locomotion speed and angular velocity. It is shown that the problem can be separated to two tractable optimization problems; one for the shape offset resulting in turning, and the other for the periodic movement resulting in locomotion along a fixed direction. The effectiveness of the method is demonstrated by a case study of a simple locomotor swimming in water.

Keywords: Optimal control, Computational methods, Optimization algorithms
Abstract: A variable-order adaptive mesh refinement method for solving optimal control problems is described. The method employs orthogonal collocation at Legendre-Gauss-Radau points. The mesh refinement method uses a previously derived convergence rate in order to modify the mesh. First, in regions where the solution is not sufficiently smooth, the method employs mesh interval refinement to place mesh points near discontinuities in the solution. Next, in regions where the solution is smooth the method increases the degree of the approximating polynomial. Furthermore, the method can decrease the size of the mesh in one of two ways. First, by representing the state using a power series approximation it is possible to decrease the required polynomial degree when it is determined that the coefficients of the highest powers of the power series are insignificant in comparison to the mesh refinement accuracy tolerance. Second, mesh intervals can be combined if it is determined that the power series representations are the same in two or more adjacent mesh intervals. Finally, the method is described in detail and is applied successfully to an example from the open literature.

Keywords: Optimal control, Nonlinear systems, Mechatronics
Abstract: This paper proposes a framework for optimal control of mechanical systems possessing conserved quantities such as control moment gyros (CMGs). It will be shown that output regulation theory is appropriate to handle such constraints and that the center-stable manifold method for solving the associated Hamilton-Jacobi equation is effective for computing the optimal feedback control. With this framework, it is possible to design robust and high performance controller for CMGs. Simulations show the effectiveness of the proposed method.

Keywords: Optimal control, Nonlinear systems, Stochastic optimal control
Abstract: The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems with more than moderate state space size due to the curse of dimensionality. This work combines recent results in the structure of the HJB, and its reduction to a linear Partial Differential Equation (PDE), with methods based on low rank tensor representations, known as a separated representations, to address the curse of dimensionality. The result is an algorithm to solve optimal control problems which scales linearly with the number of states in a system, and is applicable to systems that are nonlinear with stochastic forcing in finite-horizon, average cost, and first-exit settings. The method is demonstrated on inverted pendulum, VTOL aircraft, and quadcopter models, with system dimension two, six, and twelve respectively.

Keywords: Optimal control, Nonlinear systems
Abstract: This paper studies the optimal control of trajectories converging to or escaping from a stable equilibrium. The control duration is assumed to be short. When the control is turned off, the trajectories have not reached the target and they subsequently evolve according to the free motion dynamics. In this context, we show that the problem can be formulated as a finite-horizon optimal control problem which relies on the notion of isostables. For linear and nonlinear systems, we solve this problem using Pontryagin’s maximum principle and we study the relationship between the optimal solutions and the geometry of the isostables. Finally, optimal strategies for choosing the magnitude and duration of the control are considered.

Keywords: Electrical power systems, Predictive control for linear systems, Constrained control
Abstract: This paper presents a predictive controller for handling plug-and-play (P&P) charging requests of electric vehicles (EVs) in a distribution system. The proposed method uses a two-stage hierarchical control scheme based on a model predictive control (MPC) formulation for tracking periodic references. The first stage computes a reachable periodic reference that trades off deviation from the nominal voltage with the required generation control. The second stage computes a controller that tracks this reference and charges the EVs, while satisfying system constraints at all times. Under the assumption of a time-periodic load, it is shown that the proposed controller is recursively feasible and exponentially stable i.e. the EVs' state of charge (SOC) and bus voltages converge to the desired SOC and to the optimal periodic reference respectively. Finally, the proposed scheme is illustrated in a set of examples.

Keywords: Predictive control for linear systems, Emerging control applications, Stochastic optimal control
Abstract: Inventory management is one of the main tasks that the pharmacy department has to carry out in a hospital. It is a complex problem that requires to establish a tradeoff between different and contradictory optimization criteria. The complexity of the problem is increased due to the constraints that naturally arise in this type of applications. In this paper, which corresponds to preliminary works performed to implement advanced control techniques for pharmacy management in two Spanish hospitals, we propose and assess chance-constrained model predictive control (CC-MPC) as a mean to relieve this issue.

Keywords: Predictive control for linear systems, Optimal control, Stochastic systems
Abstract: Stochastic linear systems arise in a large number of control applications. This paper presents a mean-variance criterion for economic model predictive control (EMPC) of such systems. The system operating cost and its variance is approximated based on a Monte-Carlo approach. Using convex relaxation, the tractability of the resulting optimal control problem is addressed. We use a power management case study to compare different variations of the mean-variance strategy with EMPC based on the certainty equivalence principle. The certainty equivalence strategy is much more computationally efficient than the mean-variance strategies, but it does not account for the variance of the uncertain parameters. Open-loop simulations suggest that a single-stage mean-variance approach yields a significantly lower operating cost than the certainty equivalence strategy. In closed-loop, the single-stage formulation is overly conservative, which results in a high operating cost. For this case, a two-stage extension of the mean-variance approach provides the best trade-off between the expected cost and its variance. It is demonstrated that by using a constraint back-off technique in the specific case study, certainty equivalence EMPC can be modified to perform almost as well as the two-stage mean-variance formulation. Nevertheless, we argue that the mean-variance approach can be used both as a strategy for evaluating less computational demanding methods such as the certainty equivalence method, and as an individual control strategy when heuristics such as constraint back-off do not perform well.

Keywords: Predictive control for linear systems, Optimization algorithms, Constrained control
Abstract: This paper presents a new distributed optimization technique, the inexact fast alternating minimization algorithm (inexact FAMA), that allows for inexact local computations as well as for errors resulting from limited communications. We show that inexact FAMA is equivalent to the inexact accelerated proximal-gradient method applied to the dual problem and derive an upper-bound on the number of iterations for convergence for inexact FAMA. The second contribution of this work is that a weakened assumption for FAMA, as well as for its inexact version, is presented. The new assumption allows the strongly convex objective in the optimization problem to be subject to convex constraints, while still guaranteeing the convergence of the algorithm, which allows its applicability to control problems. We apply inexact FAMA to distributed MPC problems and derive the convergence properties of the algorithm for this special case. By employing the upper-bound on the number of iterations, sufficient conditions on the errors are provided, that ensure the convergence of the algorithm. Finally, we demonstrate the performance of the algorithm and the theoretical findings using a randomly generated distributed MPC example.

Keywords: Predictive control for linear systems, Optimization algorithms, Constrained control
Abstract: In model predictive control often the underlying optimization problem is not solved exactly to meet hard realtime bounds or to save computations. This jeopardizes properties of the closed loop system, such as stability, performance or recursive feasibility. We present a framework for linear system with polytopic constraints and quadratic performance criteria, which guarantees recursive feasibility and stability subject to inexact solutions. We combine the approach with simple optimization methods to obtain real-time feasibility and stability.

Keywords: Automotive control, Predictive control for linear systems, Optimal control
Abstract: In this paper a novel rule based controller is developed for comfort improvement of a semi-active suspension system. The controller is developed using the results from a model predictive controller (MPC) which is designed for minimal vertical acceleration, taking into account the actuator constraints. It is shown that a controller can be designed that improves ride comfort significantly and can be implemented in real-time.

Keywords: Discrete event systems, Supervisory control, Emerging control applications
Abstract: In our recent work, we proposed a series of binary decision diagram (BDD-) based approaches for developing the maximally permissive deadlock avoidance policy (DAP) for a class of complex resource allocation systems (RAS). In this paper, (i) we extend these approaches by introducing a procedure that generates a set of comprehensible ``guard'' predicates to represent the resulting DAP, and (ii) we customize them to the problem of deadlock avoidance in shared-memory multithreaded software, that has been previously addressed by the Gadara project. In the context of this last application, the generated guards can be instrumented directly into the source code of the underlying software threads, providing, thus, a very efficient and natural representation of the target policy. At the same time, by integrating the representational and computational strengths of symbolic computation, the presented approach can support the computation of the maximally permissive DAP for RAS corresponding to problem instances of even larger scale and complexity than those addressed in the current literature.

Keywords: Discrete event systems, Automata, Supervisory control
Abstract: In this paper we model an operational planning and scheduling problem under multiple job deadlines in a time-weighted automaton framework. We first present a method to determine whether all given job specifications and deadlines can be met by computing a supremal controllable job satisfaction sublanguage. When this supremal sublanguage is not empty, we compute one of its sublanguages that ensures the minimum total job earliness by adding proper delays. When this supremal sublangauge is empty, we will relax the deadlines of some job requirements, and compute a controllable minimum earliness sublanguage which satisfies all requirements and job deadlines except for those relaxed ones, and ensures the minimum total tardiness of those relaxed deadlines.

Keywords: Discrete event systems, Electrical power systems, Networked control systems
Abstract: In this paper we investigate control and management of power distribution networks modeled as timed and networked discrete event systems. We assume that the controller (the supervisor) communicates with the system to be controlled via a shared communication network, and that this network experiences bounded delays and losses that impact the controller. Under these assumptions, the necessary and sufficient condition for the existence of a controller is expressed as network controllability and network observability, which we define in the paper. We apply these results to a power distribution network, the IEEE 33-node (bus) test system, where the objective is to ensure the total substation transformer power stays within the given safety limits.

Keywords: Automata, Discrete event systems, Fault diagnosis
Abstract: We consider distributed fault diagnosis in a discrete event system modeled as a nondeterministic finite automaton that is observed, at multiple observation sites, through distinct natural projection maps. The majority of previous work in this setting has focused on local observers (diagnosers) that are separately implemented at each observation site, without exchanging any information among themselves and relying exclusively on communicating their decision (fault or no fault) to a coordinator that is responsible from making the ultimate diagnosis decision (co-diagnosability). In this work we extend recent techniques that allow local observers to communicate their state estimates to a coordinator by considering strategies that also allow the exchange of local diagnostic information among different observation sites and by analyzing their diagnosability.

Keywords: Discrete event systems, Automata
Abstract: We consider decentralized diagnosis of discrete event systems in the conditional disjunctive architecture. A notion of conditional disjunctive-codiagnosability, which guarantees the detection of any failure by a conditional disjunctive decentralized diagnoser within a bounded number of steps, has been defined in the literature. In this paper, we compute the minimum number of steps, called the delay bound, within which the occurrence of any failure can be detected by conditional disjunctive decentralized diagnosis. The delay bound is important to evaluate the ability of diagnosis. In addition, it can be used to synthesize a conditional disjunctive decentralized diagnoser for a conditional disjunctive-codiagnosable system.

Keywords: Discrete event systems, Petri nets, Linear system observers
Abstract: This paper presents a sufficient condition to solve the observation problem in tropical linear event-invariant dynamical systems, where a linear functional of the states can be observed in a finite number of steps using only the information from inputs and outputs. Using the residuation theory, this solvability condition can be easily implemented in polynomial time. Moreover, the main results are applied to state feedback control using only the observed states based on the measurements of the original states in the system. Furthermore, the main results are implemented in the perturbation observation problem for tropical linear event-invariant dynamical systems, where the system matrices are perturbed in intervals.

Keywords: Biomolecular systems, Uncertain systems, Nonlinear systems
Abstract: In this paper, we study saddle-node bifurcation and its robustness analysis for a class of nonlinear systems with dynamic uncertainties. First, we formulate a robust bifurcation analysis problem of evaluating the region that contains all potential bifurcation points on which an equilibrium appears, disappears, or loses hyperbolicity depending on uncertainties. Next, we propose an existence condition of multiple equilibria and evaluation of their location. Then, we derive a condition for robust hyperbolicity of a set of potential equilibrium points, and identify the region that contains all potential bifurcation points. The proposed analysis method is applied to robustness analysis of a genetic network model representing a mechanism for generating induced pluripotent stem cells (iPS cells). We find that saddle-node bifurcation occurs in the iPS model. Then, by the proposed robustness analysis, we further show that the bifurcation is so robust that it plays an essential role for inducing pluripotency in actual iPS cells.

Keywords: Uncertain systems, Large-scale systems, LMIs
Abstract: The performance analysis of uncertain large-scale systems is under consideration. It is performed via a hierarchical modeling and analysis of the systems thanks to the recursive application of a propagation of dissipativity properties result. In contrast to an one-step approach such as (upper bound) mu-analysis where computation time can be prohibitive for large-scale systems, the proposed method allows to set the trade-off between conservatism and computation time. The approach is used on a PLL network example and illustrates the new trade-off achieved.

Keywords: Uncertain systems, Linear systems
Abstract: This paper addresses the problem of determining the robust H-infinity norm of 2D mixed continuous-discrete-time systems affected by uncertainty. Specifically, it is supposed that the matrices of the model are polynomial functions of an unknown vector constrained into a semialgebraic set. It is shown that an upper bound of the robust H-infinity norm can be obtained via a semidefinite program (SDP) by introducing complex Lyapunov functions candidates with rational dependence on a frequency and polynomial dependence on the uncertainty. A necessary and sufficient condition is also provided to establish whether the found upper bound is tight. Some numerical examples illustrate the proposed approach.

Keywords: Uncertain systems, Modeling, Optimization
Abstract: This paper develops techniques for constructing empirical predictor models based on observations. By contrast to standard models, which yield a single predicted output at each value of the model's inputs, Interval Predictors Models (IPM) yield an interval into which the unobserved output is predicted to fall. The IPMs proposed prescribe the output as an interval valued function of the model's inputs, render a formal description of both the uncertainty in the model's parameters and of the spread in the predicted output. Uncertainty is prescribed as a hyper-rectangular set in the space of model's parameters. The propagation of this set through the empirical model yields a range of outputs of minimal spread containing all (or, depending on the formulation, most) of the observations. Optimization-based strategies for calculating IPMs and eliminating the effects of outliers are proposed. Outliers are identified by evaluating the extent by which they degrade the tightness of the prediction. This evaluation can be carried out while the IPM is calculated. When the data satisfies mild stochastic assumptions, and the optimization program used for calculating the IPM is convex (or, when its solution coincides with the solution to an auxiliary convex program), the model's reliability (that is, the probability that a future observation would be within the predicted range of outputs) can be bounded rigorously by a non-asymptotic formula.