In this work, we address the problem of designing
probabilistic robust controllers for discretetime systems whose
objective is to reach and remain in a given target set with
high probability. More precisely, given probability distributions
for the initial state, uncertain parameters and disturbances, we
develop algorithms for designing a control law that i) maximizes
the probability of reaching the target set in N steps ii)
makes the target set robustly positively invariant. To solve this problem, a sequence of
convex relaxations is provided, whose optimal value is shown
to converge to solution of the original problem. In other words,
we provide a sequence of semidefinite programs of increasing
dimension and complexity which can arbitrarily approximate
the solution of the probabilistic robust control design problem.
Probabilistically Robust Control Design
Convex Equivalent Problem:Example 1
Example 3: Probabilistic Control as Volume OptimizationMore information on volume optimization problem:
Papers Ashkan Jasour and Constantino Lagoa ”Convex Constrained Semialgebraic Volume Optimization: Application in Systems and Control”, Under submission, 2016.
Presentation Convex Relaxations of a Probabilistically Robust Control Design Problem [pdf]
52st IEEE Conference on Decision and Control, Florence, Italy, 2013
