For a class of coupled linear, time-invariant, multi-input multi-output (MIMO) systems, a systematic method is developed according to different relative degrees of system to tune the P/PI/PID control gains. By using linear quadratic regulator (LQR) strategy, the restriction of control cost can be taken into consideration for controller designs. Furthermore, the robustness of LQR provides improvement on performance of PID control. There are few literatures on the discrete-time optimal PID control.  A new error dynamic equation is established via approximation concept to construct the discrete-time optimal PID control. When the controlled plant is unknown, the comparison of the neural network (NN) and recursive least squares (RLS) model is presented for the off-line system identification. The output-sensorless optimal PID control is also discussed. When the nonlinear controlled plant is unknown except the system order (or system delay) and the sign of transmitting control input, a novel self-tuning method of optimal PID control laws is proposed based on an inequality constraint optimization mechanism to ensure the minimization of PID gains as coercing the tracking error to zero.

The internal model principle is the sufficient and necessary condition to obtain the ripple-free deadbeat control response. In this dissertation, a new deadbeat tracking controller is developed by applying the so-called gain operator. Under some derived sufficient conditions, the ripple response in the sampled-data systems will be very inconspicuous. To handle the systems with unmeasured states, the deadbeat observer will be integrated with the deadbeat tracking controller. Once the system has variations on system parameters, the performance will be destroyed due to constant control gains. Therefore, the on-line recursive least squares (RLS) algorithm is adopted to estimate the new system parameters for updating the deadbeat control parameters.

           When the system uncertainties are large, the robust control may fail to maintain a good performance. The radial basis function neural network (RBFNN) can be employed as an approximator to compensate the system uncertainties after effective learning. Then a multivariable sliding-mode neuro-adaptive control is developed for improvement on tracking performance. Two aspects affect the approximation capability of neural networks: structure and updating law. An inequality constraint optimization mechanism, minimizing the connection weights subject to the stable reaching condition, is established to adjust the connection weights of RBFNN. Moreover, the e-modification term is utilized as another part of the stable updating law to guarantee the boundedness of connection weights. The proposed stable updating law indeed improves the learning capability of RBFNN.

        All the control laws and updating laws in this dissertation were justified with stability analysis and simulations. After choosing the corresponding Lyapunov function, the system stability can be guaranteed by using Lyapunov stability theory if the derived sufficient conditions are satisfied.