Strategies for Computing Switching Feedback Controllers

We consider the problem of computing suboptimal feedback switching controllers for discrete dynamical systems. The paper shows how to combine convex optimization techniques with relaxed dynamic programming. We apply the method to several problems that have been considered recently in the literature. A particularly interesting example is given by a DC-DC converter. The proposed algorithm has several interesting properties. The main theoretical result of this paper is the introduction of a new approximate policy iteration algorithm which is shown to converge to the optimal cost function

Dynamic Model Predictive Control

In this paper an alternative approach to model predictive control is presented. In traditional MPC a finite horizon open loop optimal control problem is solved in each sampling instance. When uncertainties such as computational delays are present, one can encounter problems. We propose to parametrize the control sequence in each sampling instant in terms of a linear feedback controller, i.e. in each sample a dynamic feedback compensator is computed. Thus, if computational delays are present the control system runs in closed loop, decreasing the need for ad hoc solutions used in traditional MPC

Computation of approximate value functions for constrained control problems

The paper discusses an iterative algorithm for computing approximations to the optimal value function for constrained control problems. The algorithm gives an explicit measure on the distance to the optimal value function. A major step in the course of constructing an algorithm for these problems is to choose an efficient parameterization. The choice has several implications. The main obstacle in the algorithm we consider is that it involves an infinite-dimensional optimization problem in each step, without approximations these problems are computationally infeasible. The choice of parameterization must thus be chosen accordingly. Multivariate polynomials are a good candidate parameterization. To obtain a feasible algorithm, we impose certain convexity properties and make use of recent results on the representation of positive polynomials

Approximate Dynamic Programming with Applications

This thesis studies approximate optimal control of nonlinear systems. Particular attention is given to global solutions and to the computation of approximately optimal feedback controllers. The solution to an optimal control problem is characterized by the optimal value function. For a large class of problems the optimal value function must satisfy a Hamilton-Jacobi-Bellman type equation. Two common methods for solving such equations are policy iteration and value iteration. Both these methods are studied in this thesis.An approximate policy iteration algorithm is presented for both the continuous and discrete time settings. It is shown that the sequence produced by this algorithm converges monotonically towards the optimal value function. A multivariate polynomial relaxation algorithm is proposed for linearly constrained discrete time optimal control problems with convex cost. Relaxed value iteration is studied for constrained linear systems with convex piecewise linear cost. It is shown how an explicit piecewise linear control law can be computed and how the resulting lookup table can be reduced efficiently.The on-line implementation of receding horizon controllers, even for linear systems, is usually restricted to systems with slow dynamics. One reason for this is that the delay between measurement and actuation introduced by computing the control signal on-line can severely degrade systems with fast dynamics. A method to improve robustness against such delays and other uncertainties is presented. A case study on the control of DC--DC converters is given. Feasibility of a Relaxed Dynamic Programming algorithm is verified by synthesizing controllers for both a step-down converter and a step-up converter. The control performance is evaluated both in simulations and in real experiments

On approximate policy iteration for continuous-time systems

We propose a new algorithm for feedback nonlinear synthesis. The algorithm computes suboptimal solutions, with bounds on suboptimality, to the Hamilton-Jacobi-Bellman equation. For systems that are modeled with polynomials the computations can be done efficiently via semidefinite programming. To illustrate the strength of the proposed method, we computesmooth stabilizing feedback controllers for several problems

Hybrid Control Techniques for Switched-Mode DC-DC Converters Part II: The Step-Up Topology

International audienc

Comparison of hybrid control techniques for buck and boost DC-DC converters

WOSInternational audienceFive recent techniques from hybrid and optimal control are evaluated on two power electronics benchmark problems. The benchmarks involve a number of practically interesting operating scenarios for fixed-frequency synchronous dc-dc converters. The specifications are defined such that good performance can only be obtained if the switched and nonlinear nature of the problem is accounted for during the design phase. A nonlinear action is featured in all methods either intrinsically or as external logic. The designs are evaluated and compared on the same experimental platform. Experiments show that the proposed methods display high performances, while respecting circuit constraints, thus protecting the semiconductor devices. Moreover, the complexity of the controllers is compatible with the high-frequency requirements of the considered application