Abstract
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.
Highlights
Interest has been increasing in control systems that require limitations on the state of the target system
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 model-predictive control (MPC) to verify the effectiveness of the proposed controller
For analytical and computational convenience, the target system for industrial purposes is often linearized, several studies on linear optimal controllers with state constraints were performed. These studies imply large computational loads that make it difficult to implement in real time
Summary
Interest has been increasing in control systems that require limitations on the state of the target system. Optimal trajectory control for industrial robots [1,2], which limits the workspace for co-work between humans and machines, and optimal powertrain control for hybrid vehicle systems [3,4,5], which has limitations on battery capacity, have become more critical to industry. For analytical and computational convenience, the target system for industrial purposes is often linearized, several studies on linear optimal controllers with state constraints were performed. These studies imply large computational loads that make it difficult to implement in real time. The following section explains why these computational loads are caused
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