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Near-optimal control of discrete-time nonlinear systems with stability guarantees

Abstract : Artificial intelligence is rich in algorithms for optimal control. These generate commands for dynamical systems in order to minimize a a given cost function describing the energy of the system, for example. These methods are applicable to large classes of non-linear systems in discrete time and have proven themselves in many applications. Their application in control problems is therefore very promising. However, a fundamental question remains to be clarified for this purpose: that of stability. Indeed, these studies focus on optimality and ignore in the In most cases the stability of the controlled system, which is at the heart of control theory. The objective of my thesis is to study the stability of non-linear systems controlled by such algorithms. The stakes are high because it will create a new bridge between artificial intelligence and control theory. Stability informs us about the behaviour of the system as a function of time and guarantees its robustness in the presence of model disturbances or uncertainties. Algorithms in artificial intelligence focus on control optimality and do not exploit the properties of the system dynamics. Stability is not only desirable for the reasons mentioned above, but also for the possibility of using it to improve these intelligence algorithms artificial. My research focuses on control techniques from (approximated) dynamic programming when the system model is known. For this purpose, I identify general conditions by which it is possible to guarantee the stability of the closed-loop system. On the other hand, once stability has been established, we can use it to drastically improve the optimality guarantees of literature. My work has focused on two main areas. The first concerns the approach by iteration on values, which is one of the pillars of dynamic programming is approached and is at the heart of many reinforcement learning algorithms. The second concerns the approach by optimistic planning, applied to switched systems. I adapt the optimistic planning algorithm such that, under natural assumptions in an a stabilisation context, we obtain the stability of closed-loop systems where inputs are generated by this modified algorithm, and to drastically improve the optimality guarantees of the generated inputs.
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Mathieu Granzotto. Near-optimal control of discrete-time nonlinear systems with stability guarantees. Automatic. Université de Lorraine, 2019. English. ⟨NNT : 2019LORR0301⟩. ⟨tel-02517304⟩

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