Discrete Time Nonlinear Controller Design with Guaranteed Asymptotic Stability and Shorter Horizon Lengths

Ensuring asymptotic stability of the Nonlinear Model Predictive Control formulation is not trivial. Stabilizing ingredients such as terminal cost term and terminal set are necessary. Approaches available in the literature provide minimal degrees of freedom for the terminal set characterization. The current work presents a linear quadratic regulator based approach, which provides large degrees of freedom for enlarging the terminal set. The novel approach is suitable for a system with any state and input dimension. The proposed approach involves solving modified Lyapunov equations, which provide additive matrices as tuning parameters for enlarging the terminal set. The effectiveness of the proposed approach is demonstrated using a benchmark fermenter system and a two-state unstable system. Terminal sets obtained using the proposed approach are significantly larger than the approach from the literature, thereby reducing the prediction horizon length required for feasibility.