A Convex Analysis-Based Optimal control Framework for Industrial Automation Systems

Abstract

Industrial automated control systems are driven by coupled dynamical systems, actuator constraints, uncertain load, and conflicting objectives of precise tracking, energy conservation, and maintenance of machines. In this paper, a new framework for optimal control using convex analysis theory is developed where bounded uncertainty in operation is modeled as an adversarial disturbance, and the control problem is formulated as a convex-concave minimax problem in infinite dimensions. Through the control-to-state transformation, a saddle point problem in product Hilbert space is obtained from the constrained dynamical system. The solution of this problem is analyzed in terms of a variational inequality, a normal cone inclusion, KKT conditions, and Fenchel duality. Convexity concavity in its strong form leads to uniqueness, whereas monotonicity in its strong form results in Lipschitz stability with respect to the parameters of the plant and disturbances. A projected extragradient primal-dual algorithm is obtained, and global linear convergence is established under admissible step size choices. Experimental verification on a three-stage interconnected production line process shows that the worst-case cost is 13.84, tracking error is 0.071, the energy index is 7.62, constraint violation is zero, and convergence is achieved in 47 iterations. Compared with other control methods like model predictive control, projected-gradient control, linear-quadratic regulation, and robust H-infinity control, the presented approach outperforms them in feasibility and worst-case performance.