STOCHASTIC MODEL PREDICTIVE CONTROL WITH BOUNDED CONTROL INPUTS : A VECTOR SPACE APPROACH

This paper is concerned with the problem of Model Predictive Control (MPC) of discrete-time systems subject to random noise inputs. We pose the problem of selecting an appropriate optimal control on general separable vector spaces of functions and show that in the case of linear systems the resulting optimization problem has a tractable convex solution. Then, we show how this approach can be adapted to handle hard bounds on the control inputs for both bounded noise and possibly unbounded noise inputs. Under the assumption that the zero-input and zero-noise system is asymptotically stable, we show that the variance of the state is bounded when enforcing hard bounds on the control inputs, for both the MPC and Rolling Horizon Control (RHC) implementations. Throughout the paper we provide several examples that illustrate how quantities needed in the formulation of the resulting optimization problems can be calculated off-line.

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