## Abstract

This chapter discusses continuous-time model predictive control (CMPC) without constraints. It will take the reader through the principles of continuoustime predictive control design, and the solutions of the optimal control problem. It shows that when constraints are not involved in the design, the continuous-time model predictive control scheme becomes a state feedback control system, with the gain being chosen from minimizing a finite prediction horizon cost. The continuous-time Laguerre functions and Kautz functions discussed in Chapter 5 are utilized in the design of continuous-time model predictive control. When a set of Laguerre functions is used in the design, the desired closed-loop response can be achieved by tuning the time scaling factor *p* and the number of terms *N*. Without constraints, the model predictive control has an analytical optimal solution. Since constant input disturbance rejection and set-point following are the most commonly encountered design requirements, this chapter will treat those cases extensively by embedding an integrator in the design model. This chapter concludes with the use of Kautz functions in the design, which leads to explicit specification of the poles in the othonormal functions. Without constraints, if numerically permitted for a sufficiently large prediction horizon, this could become entirely identical to the underlying continuous-time linear quadratic regulator (LQR).

## Keywords

Model Predictive Control Linear Quadratic Regulator Prediction Horizon Control Trajectory Laguerre Function## Preview

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