The achievable region approach to the optimal control of stochastic systems (original) (raw)

1999, Journal of the Royal …

The achievable region approach seeks solutions to stochastic optimization problems by characterizing the space of all possible performances (the achievable region) of the system of interest and optimizing the overall system-wide performance objective over this space. ...

A relaxation technique to ensure feasibility in stochastic control with input and state constraints

arXiv: Optimization and Control, 2016

We consider a stochastic linear system and address the design of a finite horizon control policy that is optimal according to some average cost criterion and accounts also for probabilistic constraints on both the input and state variables. This finite horizon control problem formulation is quite common in the literature and has potential for being implemented in a receding horizon fashion according to the model predictive control strategy. Such a possibility, however, is hampered by the fact that, if the disturbance has unbounded support, a feasibility issue may arise. In this paper, we address this issue by introducing a constraint relaxation that is effective only when the original problem turns out to be unfeasible and, in that case, recovers feasibility as quickly as possible. This is obtained via a cascade of two probabilistically-constrained optimization problems, which are solved here through a computationally tractable scenario-based scheme, providing an approximate solutio...

Optimal control of ultimately bounded stochastic processes

Nagoya Mathematical Journal, 1974

We shall consider the optimal control for a system governed by a stochastic differential equationwhere u(t, x) is an admissible control and W(t) is a standard Wiener process. By an optimal control we mean a control which minimizes the cost and in addition makes the corresponding Markov process stable.

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