This paper addresses the problem of the adaptive stabilization of a nonholonomic mobile robot. A discontinuous adaptive state feedback controller is derived to achieve global stability and convergence of the trajectories of the closed loop system in the presence of parameter modeling uncertainty. This task is achieved by a non smooth transformation in the original system followed by the derivation of smooth time invariant control in the new coordinates. The stability and convergence analysis is built on Lyapunov stability theory.

The paper describes a way of determination of quadratic-optimal regulator for linear continuous and discrete systems with constraints. The method is based on direct numerical minimization of the quadratic criterion expressing the quality of control. Constant regulator matrix, independent on the starting state, is obtained as a result. Due to the constraints the optimal regulator however depends on initial state. Therefore, the problem formulation was modified by using an extended criterion of optimality that guarantees quality behavior for any initial state within a given set.

One of the typical problems in active noise control (ANC) system design is identification of an electro-acoustic plants. In the example considered models are required to parameterize an adaptive feedforward ANC system creating a local 3-dimensional zone of quiet in an enclosure. The structure of a multi-channel control system involves the necessity of identification of transfer functions for secondary and acoustic feedback paths. Plants to be identified are of MISO (Multi-Input-Single-Output) type with three inputs. The problem of designing the identification experiment is considered and different excitation signals are tested. Complexity of the plant implies that identified models should be of a very high order and the ordinary least squares method is the most applicable for model fitting in this case. Since there are no prerequisites for model structure assumption, delays and polynomial orders are to be identified too. This is done by iterative procedure of testing different structures and selection this one which minimizes the BIC criterion. The results of real-world experiments are presented and accuracy of frequency response estimates of parametric models is proved using a classical spectral analysis.

An alternative to EXACT self-tuning algorithm available in PID controllers from Emerson-Foxboro is presented. The same specifications, i.e. overshoot and damping of the error transient, are used. Tuning steps are performed along contour lines of three template surfaces which represent overshoot, damping and frequency in terms of loop gain and controller zero. The template surfaces are generated by simulation of PID loop with time-constant-plus-delay plant whose time constant is the same as delay. The algorithm applies simple 2nd order model for oscillating and damped transients. Convergence rate is similar to that of EXACT. Simplified version of the algorithm has been implemented in an industrial controller.

The problem of the state and output stabilization of discrete-time delay systems on Hilbert spaces is considered. Sufficient and necessary conditions for the state stabilization are given. Analogue results for the output stabilization are presented.
This work is organized in three sections. The state stabilization problem is examined in section 2. The three principle notions of stability and stabilizability (uniform, strong and weak) are investigated. Using the state space technique, it is shown that this problem can be tackled considering an equivalent non delayed system. Sufficient and necessary conditions for the stabilization of the new system are then established. Using these results and similar methods, sufficient and necessary conditions for the output stabilization are developed in section 3. To illustrate this work, some examples are given.

In this paper, a quasi-linear parameter-varying (quasi-LPV) model for canal control is proposed. This model relates the downstream level with the gate opening and takes into account the non-linearity, the variation of the model parameters and the dependence with the operating point. Thus, this kind of a model represents in a more accurate way the canal behavior than a linear time invariant (LTI) model. Moreover, it is suitable as for the conventional gain-scheduling as for a rigorous and formal (LPV or fuzzy) gain-scheduling control design using linear matrix inequality (LMI) tools. Finally, the proposed LPV model has been used to design a conventional gain-scheduling (GS) PI controller and tested on a single pool canal.