19 research outputs found
Approximately Optimal Controllers for Quantitative Two-Phase Reach-Avoid Problems on Nonlinear Systems
The present work deals with quantitative two-phase reach-avoid problems on
nonlinear control systems. This class of optimal control problem requires the
plant's state to visit two (rather than one) target sets in succession while
minimizing a prescribed cost functional. As we illustrate, the naive approach,
which subdivides the problem into the two evident classical reach-avoid tasks,
usually does not result in an optimal solution. In contrast, we prove that an
optimal controller is obtained by consecutively solving two special
quantitative reach-avoid problems. In addition, we present a fully-automated
method based on Symbolic Optimal Control to practically synthesize for the
considered problem class approximately optimal controllers for sampled-data
nonlinear plants. Experimental results on parcel delivery and on an aircraft
routing mission confirm the practicality of our method.Comment: 14 pages, 7 figure
Guaranteed Control of Sampled Switched Systems using Semi-Lagrangian Schemes and One-Sided Lipschitz Constants
In this paper, we propose a new method for ensuring formally that a
controlled trajectory stay inside a given safety set S for a given duration T.
Using a finite gridding X of S, we first synthesize, for a subset of initial
nodes x of X , an admissible control for which the Euler-based approximate
trajectories lie in S at t [0,T]. We then give sufficient conditions
which ensure that the exact trajectories, under the same control, also lie in S
for t [0,T], when starting at initial points 'close' to nodes x. The
statement of such conditions relies on results giving estimates of the
deviation of Euler-based approximate trajectories, using one-sided Lipschitz
constants. We illustrate the interest of the method on several examples,
including a stochastic one
Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction
We show that, for any spatially discretized system of reaction-diffusion, the
approximate solution given by the explicit Euler time-discretization scheme
converges to the exact time-continuous solution, provided that diffusion
coefficient be sufficiently large. By "sufficiently large", we mean that the
diffusion coefficient value makes the one-sided Lipschitz constant of the
reaction-diffusion system negative. We apply this result to solve a finite
horizon control problem for a 1D reaction-diffusion example. We also explain
how to perform model reduction in order to improve the efficiency of the
method