Electrical and Electronic Engineering - Research Publications

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End date: 2022 × Start date: 2020 × Author: Nesic, Dragan × Author: Granzotto, Mathieu × Type: Journal Article ×

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    Stable Near-Optimal Control of Nonlinear Switched Discrete-Time Systems: An Optimistic Planning-Based Approach
    Granzotto, M ; Postoyan, R ; Busoniu, L ; Nesic, D ; Daafouz, J (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2022-05)
    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, 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 near-optimality 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 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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    Finite-horizon discounted optimal control: stability and performance
    Granzotto, 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 discrete-time systems whose inputs minimize a discounted finite-horizon cost. We assume that the system satisfies stabilizability and detectability properties with respect to the stage cost. Then, a Lyapunov function for the closed-loop 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, infinite-horizon and finite-horizon costs respectively, which appear to be very different from those available in the literature.