Based on the essence of modern control algorithms:
Based on the plant controlled subsystem model (without u, Ax) + control system analysis method (with u, Ax+Bu) (generally feedback control, let u = kx) --> closed-loop control system: (A+Bk )x, that is, Acl*x; the equation can be written according to the desired control performance; finally, k (controller parameter) can be obtained by solving:
1. Steady-state performance: Stability: Lyapunov function (bounded stability, asymptotic stability, exponential stability; global stability, local stability;); steady-state error (ess);
2. Transient performance: limited time, fixed time; smoothness (overshoot, fluctuation, oscillation);
3. Energy consumption;
1. How to take the Lyapunov function to prove the state (partial or all), adaptive parameter convergence
2. How to select which parameters need to be adaptive, and how to obtain the adaptive law.