Numerical solution for strict tracking control asymptotic stability problem of MIMO systems manipulated by hard actuation constraints

Abstract

Nonlinear Multi-Input Multi-Output (MIMO) systems governed by Newtonian mechanics face significant challenges in tracking control design, especially due to actuator saturation constraints that can undermine asymptotic stability by yielding nullified control inputs. This paper proposes a novel tracking control algorithm ensuring stability and compliance with actuator limitations. The approach transforms continuous-time dynamics into a discrete-time framework, enhancing computational efficiency by replacing differential equations with algebraic ones. A sliding surface with dynamically tunable parameters is introduced for each output to optimize tracking performance, and control inputs are derived using a power reaching law, split into position and velocity modes which helps reducing actuator power and overshoot/undershoot. Actuator saturation is explicitly addressed for both modes through convex inequality constraints, enabling an optimal desired trajectory to return feasible control inputs that respect input limits while preserving asymptotic stability. A search mechanism optimizes sliding and power-reaching parameters to minimize tracking error, aligning the modified trajectory with the reference. Mathematical proofs establish the closed-loop system’s asymptotic stability and convergence of modified trajectory to reference trajectory. MATLAB simulations included by comparative investigations confirm precise tracking, robustness against parametric uncertainties, and adherence to saturation constraints, achieved without manual tuning and pre-setting. This self-tuning capability, distinguishes the method from existing approaches reliant on empirical adjustments. Real-time execution analysis validates feasibility, meeting a 0.01-second execution target. Given the quadratic relationship between search gridding intensity and computational load demonstrated through real-time execution assessment, as it provides a benchmark on parameter selection, enabling an effective balance between control performance and stringent demands of real-time feasibility. The algorithm’s adaptability to different optimization techniques to balance computational load and tracking accuracy, offers a standardized, versatile framework for controlling complex nonlinear MIMO systems in the presence of various constraints.