1. Nonlinear Predictive Control for Fast Constrained Systems By Ahmed Youssef

2. What’s MBPC Introduction CV: controlled variableMV: manipulated variable

3. Introduction Shortcomings of current industrial nonlinear MBPC Computing the MBPC control law demands significant on-line computation effort Inability to deal explicitly with the plant model uncertainty. Objective of research work Reducing the computational complexity of nonlinear MBPC & adding the robustness property whilst preserving its good attributes to make it more effective practical tool for controlling systems of fast- constrained dynamics.

4. Given the nonlinear dynamic model Reformulate into nonlinear state-dependent form This is not a linearisation Trivial example State Dependent State-Space Models

5. Hamilton-Jacobi-Bellman

6. The NLQGPC quadratic infinite horizon cost function: The optimal control vector in terms of the states of the system and reference model: NLQGPC Control Law

7. The Coupled Algebraic Riccati Equations

8. Control Lyapunov Function A C 1 function V(x):  n   is said to be a discrete CLF for the system: if V(x) is positive definite, unbounded, and if for all x  0 Dealing with Stability Issue

9. Satisficing is based on a point-wise cost / benefit comparison of an action. The benefits are given by the “Selectability” function P s (u,x), while the costs are given by the “Rejectability” function P r (u,x). The “satisficing” set is those options for which selectability exceeds rejectability: Stability via Satisficing

10. Satisficing generates the state dependent set of controls that render the closed-loop system stable with respect to a known CLF. CLF-Based Satisficing Technique

11. Magnitude Saturation Rate-Limited Actuators Actuator Dead-Zone Therefore the common term is the Saturation function Dealing with Input Constraints Examples of Actuator Constraints

12. the actuator range of operation is limited L imiting functions that map the interval (- ,  ) onto (0, 1) L imiting functions that map the interval (- ,  ) onto (-1, 1) Approximation of Magnitude Saturation

13. Error function(Blue) Tanh function(Green) Sigmoid function(Red) Sigmoid function(Black) Approximation of Magnitude Saturation

14. Case Studies F-8 fighter aircraft F-16 fighter aircraft Caltech Ducted Fan

15. Controlling of F-8 Fighter

19. CONCLUSIONS Properties of NLQGPC controller: 1. High performance 2. Less computational burden 3. Dealing with input constraints 4. Guaranteeing asymptotic stability to the closed-loop system. 5.Possesses both performance robustness & stability robustness