Design, Control and Optimization of Nonlinear Dynamic Systems

All physical systems are nonlinear, and, there are inherent physical limits on states x, outputs y and controls u. All consistently designed physical systems are controllable, and, many systems are open-loop stable. Practical solutions and control schemes are found to stabilize systems if marginal stability, metastability and instabilities in small are observed. Proportional-integral-derivative and state feedback controllers can be designed and reconfigured to ensure near-optimal governance physical systems M (x,y,u). Challenges and impediments arise in MIMO systems which exhibit multi-axis-coupling, instabilities, resonance, flexible modes, unsteady flows, sensitivity, etc. A physical controllability is always guaranteed in adequately designed systems.