Observer-based control of uncertain systems with non-linear uncertainties

Global asymptotic stabilization of nominally linear uncertain systems is considered where uncertain elements in the plant are modelled as cone bounded non-linearities. At first, a linear time-invariant state feedback law ensuring global asymptotic closed-loop stability is obtained. The algorithm which calculates such a feedback law is simple and straightforward. It does not involve repeated solutions of a parameter-dependent algebraic Riccati or any such non-linear equations. Any state feedback law thus developed can then be implemented via an observer specially designed to preserve the global asymptotic stability of the closed-loop system.     

Global stabilization with almost disturbance decoupling of a class of uncertain non-linear systems

In this paper we study the global stabilization of a class of non-linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy. The class of non-linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order. Although the plants considered are non-linear, the compensator developed here is linear. Our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback. Model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so-called ‘matching conditions’ and/or by treating a family of plants  for which a single controller simultaneously globally exponentially stabilizes all the plants in  while achieving almost disturbance decoupling of the output.     

Simultaneous External and Internal Stabilization for Continuous and Discrete-Time Critically Unstable Linear Systems with Saturating Actuators

The issues arising in hybrid or simultaneous external as well as internal stabilization of linear systems with saturating actuators are considered. Four different stabilization problems are studied. Roughly, these problems are (1) simultaneous semi-global external as well as semi-global internal stabilization, (2) simultaneous semi-global external as well as global internal stabilization, (3) simultaneous global external as well as semi-global internal stabilization, and (4) simultaneous global external as well as global internal stabilization. As evident from the literature, the requirement of internal stabilization alone either in the global or semi-global sense demands that the linear part of the given system be (a) stabilizable, and (b) has all its poles in the closed left half complex plane for continuous-time systems while it has all its poles inside and/or on the unit circle for discrete-time systems. This implies that the posed simultaneous stabilization problems are solvable at best only under the conditions (a) and (b). Under such conditions, we construct here explicit state as well as measurement feedback controllers for all the four problems in the case of continuous-time systems, and for the problems (1), (2) and (4) in the case of discrete-time systems. The design methodologies used to construct appropriate feedback laws are based on by now familiar low-gain and low-and-high gain design concepts or certain scheduled versions of them.     

Special coordinate basis for multivariable linear systems—finite and infinite zero structure,squaring down and decoupling

A special coordinate basis for multivariable linear systems is introduced here. Several fundamental properties of linear systems regarding controllability (stabiliza-bility), observability (detectability), invariant zeros, decoupling zeros, infinite zero structure, effect of feedback on zero structure, squaring down, diagonal and triangular decoupling etc. can be directly displayed in terms of the special coordinate basis. Moreover, connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established.     

Sensitivity comparison of optimal controls†

The performance index sensitivity is analysed for the general optimal control problem with initial and final target manifolds. The sensitivity is compared for two arbitrary controllers A and B which are optimal for a nominal parameter value. The method of analysis provides additional insight into the relationship between trajectory sensitivity and the sensitivity of the performance functional. An expression relating the performance index sensitivities for two designs is formulated in terms of the trajectory sensitivities at the initial and final manifolds.     

Near-optimum regulator design of singularly perturbed systems via Chandrasekhar equations

The singular perturbation theory provides a powerful design and analysis approach for model order reduction. Another method of simplifying the calculation of feedback gains in an LQG problem is the Chandrasekhar algorithm, which replaces the usual Riccati approach. The method presented in this paper combines the advantages inherent in the singular perturbation theory with those of the Chandrasekhar algorithm. This is accomplished by using lower dimensional Chandrasekhar equations for calculating the asymptotic expansion terms of the feedback gains. Two alternative design procedures are given. In one procedure the fast or boundary layer gains are calculated first followed by the slow or reduced gains. In the other procedure a more conventional design sequence is adopted. That is, first the reduced problem is solved and the boundary layer correction terms are added later on if needed.     

A singular perturbation canonical form of invertible systems: determination of multivariate root-loci

A new canonical form of multivariable invertible systems is given. This form is suitable for the singular perturbation analysis of such singular problems as multi-variable asymptotic root-loci under high-gain feedback, cheap control, state variable estimation with weak measurement noise, etc. Appropriate selection and decomposition of state variables into slow and fast changing groups is a key feature that loads to well-defined singular perturbation models. The selection of state variables is accomplished without explicitly calculating any eigenvalues of the given system but by knowing the direct relationship of the output and its differential coefficients with the input. The use of the canonical form to characterize the multivariable root-loci under high-gain feedback is demonstrated.