Observer design for systems with an energy-preserving non-linearity

Observer design is considered for a class of non-linear systems whose non-linear part is energy preserving. A strategy to construct convergent observers for this class of non-linear system is presented. The approach has the advantage that it is possible, via convex programming, to prove whether the constructed observer converges, in contrast to several existing approaches to observer design for non-linear systems. Finally, the developed methods are applied to the Lorenz attractor and to a low order model for shear fluid flow

Gradient-Bounded Dynamic Programming with Submodular and Concave Extensible Value Functions

We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value function of the dynamic program is concave extensible and submodular in its state-space, we present a new algorithm that computes deterministic upper and stochastic lower bounds of the value function similar to dual dynamic programming. We then show that the proposed algorithm terminates after a finite number of iterations. Finally, we demonstrate the efficacy of our approach on a high-dimensional numerical example from delivery slot pricing in attended home delivery.Comment: 6 pages, 2 figures, accepted for IFAC World Congress 202

Strong Stationarity Conditions for Optimal Control of Hybrid Systems

We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine system can be written as the optimizer of a mathematical program which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.Comment: 30 pages, 4 figure