Infinite horizon formulations of model predictive control (IHMPC) are known to guarantee nominal stability and optimality of the closed-loop system. All the existing algorithms for optimal IHMPC rely on the assumption that the steady-state operating point lies strictly in the interior of the feasible region. In practice, however, this assumption is often violated for a number of reasons. First, the desired input and output targets are usually computed by a global economic optimizer, which often uses linear programs (LP), pushing the desired targets to the edge of the feasible region. Second, when disturbances enter the plant, it is often the case that one or more manipulated inputs saturate during a period of steady-state operation. In such common cases, an invariant region cannot be found, and the only suboptimal solutions available are based on a finite horizon with terminal constraint or an infinite horizon with suboptimal parameterization. In this paper, we present a methodology for finding the optimal solution of the IHMPC problem when steady-state constraints are active. Our approach is to construct two finite- dimensional bounding problems that approximate the optimal solution – one from below and one from above – and to show that these bounding approximations converge to the solution of the optimal problem as the horizon increases. The algorithm guarantees that the solution can be found with any desired accuracy. Since the optimal solution of the constrained optimization problem is found, the proposed controller guarantees better performance than existing solutions. Moreover, since the nominal open-loop and the closed-loop trajectories are equal, the controller is simple to tune and understand.

Infinite Horizon Model Predictive Control with Active Steady-State Constraints

PANNOCCHIA, GABRIELE
;
2001

Abstract

Infinite horizon formulations of model predictive control (IHMPC) are known to guarantee nominal stability and optimality of the closed-loop system. All the existing algorithms for optimal IHMPC rely on the assumption that the steady-state operating point lies strictly in the interior of the feasible region. In practice, however, this assumption is often violated for a number of reasons. First, the desired input and output targets are usually computed by a global economic optimizer, which often uses linear programs (LP), pushing the desired targets to the edge of the feasible region. Second, when disturbances enter the plant, it is often the case that one or more manipulated inputs saturate during a period of steady-state operation. In such common cases, an invariant region cannot be found, and the only suboptimal solutions available are based on a finite horizon with terminal constraint or an infinite horizon with suboptimal parameterization. In this paper, we present a methodology for finding the optimal solution of the IHMPC problem when steady-state constraints are active. Our approach is to construct two finite- dimensional bounding problems that approximate the optimal solution – one from below and one from above – and to show that these bounding approximations converge to the solution of the optimal problem as the horizon increases. The algorithm guarantees that the solution can be found with any desired accuracy. Since the optimal solution of the constrained optimization problem is found, the proposed controller guarantees better performance than existing solutions. Moreover, since the nominal open-loop and the closed-loop trajectories are equal, the controller is simple to tune and understand.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/243953
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