 Electrical and Electronic Engineering  Research Publications
Electrical and Electronic Engineering  Research Publications
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ItemExploiting homogeneity for the optimal control of discretetime systems: Application to value iterationGranzotto, M ; Postoyan, R ; Busoniu, L ; Nesic, D ; Daafouz, J (IEEE, 2021)To investigate solutions of (near)optimal control problems, we extend and exploit a notion of homogeneity recently proposed in the literature for discretetime systems. Assuming the plant dynamics is homogeneous, we first derive a scaling property of its solutions along rays provided the sequence of inputs is suitably modified. We then consider homogeneous cost functions and reveal how the optimal value function scales along rays. This result can be used to construct (near)optimal inputs on the whole state space by only solving the original problem on a given compact manifold of a smaller dimension. Compared to the related works of the literature, we impose no conditions on the homogeneity degrees. We demonstrate the strength of this new result by presenting a new approximate scheme for value iteration, which is one of the pillars of dynamic programming. The new algorithm provides guaranteed lower and upper estimates of the true value function at any iteration and has several appealing features in terms of reduced computation. A numerical case study is provided to illustrate the proposed algorithm.

ItemWhen to stop value iteration: stability and nearoptimality versus computationGranzotto, M ; Postoyan, R ; Nešić, D ; Buşoniu, L ; Daafouz, J ( 20201119)Value iteration (VI) is a ubiquitous algorithm for optimal control, planning, and reinforcement learning schemes. Under the right assumptions, VI is a vital tool to generate inputs with desirable properties for the controlled system, like optimality and Lyapunov stability. As VI usually requires an infinite number of iterations to solve general nonlinear optimal control problems, a key question is when to terminate the algorithm to produce a “good” solution, with a measurable impact on optimality and stability guarantees. By carefully analysing VI under general stabilizability and detectability properties, we provide explicit and novel relationships of the stopping criterion’s impact on nearoptimality, stability and performance, thus allowing to tune these desirable properties against the induced computational cost. The considered class of stopping criteria encompasses those encountered in the control, dynamic programming and reinforcement learning literature and it allows considering new ones, which may be useful to further reduce the computational cost while endowing and satisfying stability and nearoptimality properties. We therefore lay a foundation to endow machine learning schemes based on VI with stability and performance guarantees, while reducing computational complexity.

ItemActive Learning for Linear ParameterVarying System IdentificationChin, R ; Maass, AI ; Ulapane, N ; Manzie, C ; Shames, I ; Nešić, D ; Rowe, JE ; Nakada, H ( 20200502)Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parametervarying systems. We extend existing approaches found in literature to multipleinput multipleoutput systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine airpath model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.

ItemTracking and regret bounds for online zerothorder Euclidean and Riemannian optimisationMaass, AI ; Manzie, C ; Nesic, D ; Manton, JH ; Shames, I ( 20201001)We study numerical optimisation algorithms that use zerothorder information to minimise timevarying geodesicallyconvex cost functions on Riemannian manifolds. In the Euclidean setting, zerothorder algorithms have received a lot of attention in both the timevarying and timeinvariant cases. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalisation of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimise the algorithm’s performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimisation setting. To the best of our knowledge, these are the first regret bounds even for the Euclidean version of the problem. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.

ItemOn the Latency, Rate and Reliability Tradeoff in Wireless Networked Control Systems for IIoTLiu, W ; Nair, G ; Li, Y ; Nesic, D ; Vucetic, B ; Poor, HV ( 20200701)Wireless networked control systems (WNCSs) provide a key enabling technique for Industry Internet of Things (IIoT). However, in the literature of WNCSs, most of the research focuses on the control perspective, and has considered oversimplified models of wireless communications which do not capture the key parameters of a practical wireless communication system, such as latency, data rate and reliability. In this paper, we focus on a WNCS, where a controller transmits quantized and encoded control codewords to a remote actuator through a wireless channel, and adopt a detailed model of the wireless communication system, which jointly considers the interrelated communication parameters. We derive the stability region of the WNCS. If and only if the tuple of the communication parameters lies in the region, the average cost function, i.e., a performance metric of the WNCS, is bounded. We further obtain a necessary and sufficient condition under which the stability region is nbounded, where n is the control codeword blocklength. We also analyze the average cost function of the WNCS. Such analysis is nontrivial because the finitebit controlsignal quantizer introduces a nonlinear and discontinuous quantization function which makes the performance analysis very difficult. We derive tight upper and lower bounds on the average cost function in terms of latency, data rate and reliability. Our analytical results provide important insights into the design of the optimal parameters to minimize the average cost within the stability region.

ItemOn Joint Reconstruction of State and InputOutput Injection Attacks for Nonlinear SystemsYang, T ; Murguia, C ; Lv, C ; Nesic, D ; Huang, C ( 20210308)We address the problem of robust state reconstruction for discretetime nonlinear systems when the actuators and sensors are injected with (potentially unbounded) attack signals. Exploiting redundancy in sensors and actuators and using a bank of unknown input observers (UIOs), we propose an observerbased estimator capable of providing asymptotic estimates of the system state and attack signals under the condition that the numbers of sensors and actuators under attack are sufficiently small. Using the proposed estimator, we provide methods for isolating the compromised actuators and sensors. Numerical examples are provided to demonstrate the effectiveness of our methods.

ItemNo Preview AvailableStable NearOptimal Control of Nonlinear Switched DiscreteTime Systems: An Optimistic PlanningBased ApproachGranzotto, M ; Postoyan, R ; Busoniu, L ; Nesic, D ; Daafouz, J (IEEEINST ELECTRICAL ELECTRONICS ENGINEERS INC, 20220501)Originating in the artificial intelligence literature, optimistic planning(OP) is an algorithm that generates nearoptimal control inputs for generic nonlinear discretetime systems whose input set is finite. This technique is therefore relevant for the nearoptimal control of nonlinear switched systems for which the switching signal is the control, and no continuous input is present. However, OP exhibits several limitations, which prevent its desired application in a standard control engineering context, as it requires for instance that the stage cost takes values in [0,1], an unnatural prerequisite, and that the cost function be discounted. In this paper, we modify OP to overcome these limitations, and we call the new algorithm OPmin. New nearoptimality and performance guarantees for OPmin are derived, which have major advantages compared to those originally given for OP. We also prove that a system whose inputs are generated by OPmin in a recedinghorizon fashion exhibits stability properties. As a result, OPmin provides a new tool for the nearoptimal, stable control of nonlinear switched discretetime systems for generic cost functions.

ItemFinitehorizon discounted optimal control: stability and performanceGranzotto, M ; Postoyan, R ; Busoniu, L ; Nesic, D ; Daafouz, J (Institute of Electrical and Electronics Engineers (IEEE), 2021)Motivated by (approximate) dynamic programming and model predictive control problems, we analyse the stability of deterministic nonlinear discretetime systems whose inputs minimize a discounted finitehorizon cost. We assume that the system satisfies stabilizability and detectability properties with respect to the stage cost. Then, a Lyapunov function for the closedloop system is constructed and a uniform semiglobal stability property is ensured, where the adjustable parameters are both the discount factor and the horizon length, which corresponds to the number of iterations for dynamic programming algorithms like value iteration. Stronger stability properties such as global exponential stability are also provided by strengthening the initial assumptions. We give bounds on the discount factor and the horizon length under which stability holds. In addition, we provide new relationships between the optimal value functions of the discounted, undiscounted, infinitehorizon and finitehorizon costs respectively, which appear to be very different from those available in the literature.

ItemAsynchronous Distributed Optimization via Dual Decomposition and Block Coordinate Subgradient MethodsLin, Y ; Shames, I ; Nesic, D (IEEEINST ELECTRICAL ELECTRONICS ENGINEERS INC, 20210901)In this article, we study the problem of minimizing the sum of potentially nondifferentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the behavior of an asynchronous algorithm based on dual decomposition and block coordinate subgradient methods under assumptions weaker than those used in the literature. At the same time, we allow different agents to use local stepsizes with no global coordination. Sufficient conditions are provided for almost sure convergence to the solution of the optimization problem. Under additional assumptions, we establish a sublinear convergence rate that, in turn, can be strengthened to the linear convergence rate if the problem is strongly convex and has Lipschitz gradients. We also extend available results in the literature by allowing multiple and potentially overlapping blocks to be updated at the same time with nonuniform and potentially timevarying probabilities assigned to different blocks. A numerical example is provided to illustrate the effectiveness of the algorithm.

ItemObserving the Slow States of General Singularly Perturbed SystemsDeghat, M ; Nesic, D ; Teel, AR ; Manzie, C (IEEE, 20200101)This paper studies the behaviour of observers for the slow states of a general singularly perturbed system  that is a singularly perturbed system which has boundarylayer solutions that do not necessarily converge to a slow manifold. The solutions of the boundarylayer system are allowed to exhibit persistent (e.g. oscillatory) steadystate behaviour which are averaged to obtain the dynamics of the approximate slow system. It is shown that if an observer has certain properties such as asymptotic stability of its error dynamics on average, then it is practically asymptotically stable for the original singularly perturbed system.