Electrical and Electronic Engineering - Research Publications
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ItemObserving the Slow States of General Singularly Perturbed Systems(IEEE, 2020)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 boundary-layer solutions that do not necessarily converge to a slow manifold. The solutions of the boundary-layer system are allowed to exhibit persistent (e.g. oscillatory) steady-state 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.
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ItemAn Approach to Minimum Attention Control by Sparse Derivative(IEEE, 2020)Minimum attention control proposed by Brockett is an important formulation for resource-aware control, while his problem formulation and the underlying optimization problem that he proposed is in general very hard. In this paper, we propose a computationally tractable design method of minimum attention control based on promoting sparsity of the derivative of control. The optimal control problem is formulated as L0 norm minimization of the time derivative of control under the constraint that the derivative is bounded by a fixed value. This is a non-convex problem, and we propose L1 relaxation for linear systems to obtain optimal control by efficient numerical computation. We then show equivalence theorems between the L0 and L1 optimal controls. Also, we present an example of feedback control for the first-order integrator, that illustrates the proposed methodology.
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ItemSampled-data extremum-seeking control for optimization of constrained dynamical systems using barrier function methods(IEEE, 2020-03-12)Most extremum-seeking control approaches focus solely on the problem of finding the extremum of some unknown, steady-state performance map. However, many industrial applications also have to deal with constraints on operating conditions due to, e.g., actuator limitations, limitations on design or tunable system parameters, or constraints on measurable signals. These constraints, which can be unknown a-priori, may conflict with the otherwise optimal operational condition, and should be taken into account in performance optimization. In this work, we propose a sampled-data extremum-seeking approach for optimization of constrained dynamical systems using barrier function methods, where both the objective function and the constraint function are available through measurement only. We show that, under the assumption that initialization does not violate constraints, the interconnection between a constrained dynamical system and optimization algorithms that employ barrier function methods is stable, the constraints are satisfied, and optimization is achieved. We illustrate the results by means of a numerical example.
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ItemA unifying event-triggered control framework based on a hybrid small-gain theorem(IEEE, 2020-12-14)We propose a unifying emulation-based design framework for the event-triggered control of nonlinear systems that is based on a hybrid small-gain perspective. We show that various existing event-triggered controllers fit the unifying perspective. Moreover, we demonstrate that the flexibility offered by our approach can be used for the development of novel event-triggered schemes and for a systematic modification and improvement of existing schemes. Finally, we illustrate via a simulation example that these novel and/or modified event-triggered controllers can lead to a reduction in the required number of transmissions, while still guaranteeing the same stability properties.
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ItemStochastic stabilisation and power control for nonlinear feedback loops communicating over lossy wireless networks(IEEE, 2020)We study emulation-based stabilisation of nonlinear networked control systems communicating over multiple wireless channels subject to packet loss. Specifically, we establish sufficient conditions on the rate of transmission that guarantee Lp stability-in-expectation of the overall closed-loop system. These conditions depend on the cumulative dropout probability of the network nodes for static protocols. We use the obtained stability results to study power control, where we show there are interesting trade-offs between the transmission rate, transmit power, and stability. Lastly, numerical examples are presented to illustrate our results.
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ItemA Multi-observer Approach for Parameter and State Estimation of Nonlinear Systems with Slowly Varying Parameters(ELSEVIER, 2020-01-01)This manuscript addresses the parameter and state estimation problem for continuous time nonlinear systems with unknown slowly time-varying parameters, which are assumed to belong to a known compact set. The problem is tackled by using the multi-observer approach under the supervisory framework, which generates parameter and state estimates by using a finite number of sample points of the parameter set, a bank of observers, a set of monitoring signals and a selection criterion. This note proposes a novel dynamic sampling policy for the multi-observer technique and studies its convergence properties. We prove that the parameter and state estimation errors are ultimately bounded where the ultimate bounds can be made arbitrarily small if the parameter varies sufficiently slowly, and the number of samples is sufficiently large.
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ItemActive Learning for Linear Parameter-Varying System Identification(ELSEVIER, 2020-01-01)Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output 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 air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.
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ItemAsynchronous Distributed Optimization via Dual Decomposition and Block Coordinate Ascent(IEEE, 2020-03-12)We study a class of distributed optimization problems of minimizing the sum of potentially non-differentiable convex objective functions (without requiring strong convexity). A novel approach to the analysis of asynchronous distributed optimization is developed. An iterative algorithm based on dual decomposition and block coordinate ascent is implemented in an edge based manner. We extend available results in the literature by allowing multiple and potentially overlapping blocks to be updated at the same time with non-uniform probabilities assigned to different blocks. Sublinear convergence with probability one is proved for the algorithm under the aforementioned weak assumptions. A numerical example is provided to illustrate the effectiveness of the algorithm.
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ItemOptimistic planning for the near-optimal control of nonlinear switched discrete-time systems with stability guarantees(IEEE, 2020-03-12)Originating in the artificial intelligence literature, optimistic planning (OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is therefore relevant for the near-optimal control of nonlinear switched systems, for which the switching signal is the control. However, OP exhibits several limitations, which prevent its application in a standard control context. First, it requires the stage cost to take values in [0, 1], an unnatural prerequisite as it excludes, for instance, quadratic stage costs. Second, it requires the cost function to be discounted. Third, it applies for reward maximization, and not cost minimization. In this paper, we modify OP to overcome these limitations, and we call the new algorithm OPmin. We then make stabilizability and detectability assumptions, under which we derive near-optimality guarantees for OPmin and we show that the obtained bound has major advantages compared to the bound originally given by OP. In addition, we prove that a system whose inputs are generated by OPmin in a receding-horizon fashion exhibits stability properties. As a result, OPmin provides a new tool for the near-optimal, stable control of nonlinear switched discrete-time systems for generic cost functions.
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ItemStability guarantees for nonlinear discrete-time systems controlled by approximate value iteration(IEEE, 2020-03-12)Value iteration is a method to generate optimal control inputs for generic nonlinear systems and cost functions. Its implementation typically leads to approximation errors, which may have a major impact on the closed-loop system performance. We talk in this case of approximate value iteration (AVI). In this paper, we investigate the stability of systems for which the inputs are obtained by AVI. We consider deterministic discrete-time nonlinear plants and a class of general, possibly discounted, costs. We model the closed-loop system as a family of systems parameterized by tunable parameters, which are used for the approximation of the value function at different iterations, the discount factor and the iteration step at which we stop running the algorithm. It is shown, under natural stabilizability and detectability properties as well as mild conditions on the approximation errors, that the family of closed-loop systems exhibit local practical stability properties. The analysis is based on the construction of a Lyapunov function given by the sum of the approximate value function and the Lyapunov-like function that characterizes the detectability of the system. By strengthening our conditions, asymptotic and exponential stability properties are guaranteed.