An algebraic and suboptimal solution of constrained model predictive control via tangent hyperbolic function

• Published in: Asian journal of control Vol. 23; no. 5; pp. 2420 - 2430
• Main Authors: Dursun, Ufuk, Yıldız Taşçıkaraoğlu, Fatma, Üstoğlu, İlker
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc 01-09-2021
• Subjects: Algebra; Computational efficiency; Computing time; Constrained Optimal Control; Constraints; Continuity (mathematics); Hyperbolic functions; Input Constraint; Model Predictive Control; Optimal control; Optimization; Predictive control; Saturation‐like Function; State Constraint; Tangent Hyperbolic
• ISSN: 1561-8625; 1934-6093
• DOI: 10.1002/asjc.2357

In this paper, we propose a novel method to solve the model predictive control (MPC) problem for linear time‐invariant (LTI) systems with input and output constraints. We establish an algebraic control rule to solve the MPC problem to overcome the computational time of online optimization methods. For this purpose, we express system constraints as a continuous function through the tangent‐hyperbolic function, hence the optimization problem is reformulated. There are two steps for the solution of the optimization problem. In the first step, the optimal control signal is determined by the use of the necessary condition for optimality, assuming that there is only input constraint. In the latter, the solution obtained in the first step is revised to keep the system states in a feasible region. It is shown that the solution is suboptimal. The proposed solution method is simulated for three different sample systems, and the results are compared with the classical MPC, which show that the new algebraic method dramatically reduces the computational time of MPC.