State-Constrained Sub-Optimal Tracking Controller for Continuous-Time Linear Time-Invariant (CT-LTI) Systems and Its Application for DC Motor Servo Systems

In this paper, we propose an analytic solution of state-constrained optimal tracking control problems for continuous-time linear time-invariant (CT-LTI) systems that are based on model-based prediction, the quadratic penalty function, and the variational approach. Model-based prediction is a concept taken from model-predictive control (MPC) and this is essential to change the direction of calculation for the solution from backward to forward. The quadratic penalty function plays an important role in deriving the analytic solution since it can transform the problem into a form that does not have inequality constraints. For computational convenience, we also propose a sub-optimal controller derived from the steady-state approximation of the analytic solution and show that the proposed controller satisfies the Lyapunov stability. The main advantage of the proposed controller is that it can be implemented in real time with a lower computational load compared to the implicit MPC. Finally, the simulation results for a DC motor servo system are shown and compared with the results of the direct multi-shooting method and the implicit MPC to verify the effectiveness of the proposed controller.

MULTI-OPTIONS BIDDING STRATEGY IN DISTRIBUTED ENVIRONMENT

When a Make-To-Order (MTO) enterprise receives a bidding invitation from a customer, he does not know the demand is price-sensitive or time-sensitive. In order to increase the possibility of winning this contingent order, the enterprise tenders his bid with two options characterized with price and delivery time. One is for time-sensitive demand, and it ensures that the products will be delivered as soon as possible. The other is for price-sensitive demand, and it ensures that the products will be produced at the lowest cost. The enterprise is comprised of several plants that jointly produce custom products and each plant's decision is made in a distributed way. Hence, the enterprise has to coordinate the production plans of these plants to generate the two options. Since Analytical Target Cascading (ATC) can solve multi-level hierarchical distributed problem and its convergence is proven, it is adopted to coordinate the plants' planning. This paper proposes a unique bidding option generating process in which an extended ATC model is utilized to produce time-sensitive and price-sensitive options by adjusting the coefficient of delivery tardiness. The numerical study in this paper demonstrates (1) the extended ATC model works effectively; (2) ATC with augmented Lagrangian relaxation (AL-ATC) is more effective in producing solutions than ATC with quadratic penalty function (QP-ATC); (3) ATC is an effective coordination tool by comparing the solutions made by ATC and All-In-One (AIO).