Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

Algorithm 2

Modified Step of Algorithm 1 for solving switched linear quadratic optimal control problems.

Step 2. Compute the corresponding continuous control

 (a) Solve the matrix Riccati equations (46)–(52)

 backward from to ;

 (b) Solve the auxiliary equations (47)–(53) backward

 from to ;

 (c) Solve the state equation (56) forward;

 (d) Calculate (42) and (51);

 (e) Calculate the continuous optimal control (55);