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This paper considers a linear continuous- or discrete-time dynamic object in the absence of its mathematical model. As is demonstrated below, a control law that suboptimally damps initial and (or) exogenous disturbances of such objects can be implemented based on experimental and a priori data. The approach involves the methods of robust control design and duality theory as well as the technique of linear matrix inequalities. [ABSTRACT FROM AUTHOR]

This paper develops a novel unified approach to designing suboptimal robust control laws for uncertain objects with different criteria based on a priori information and experimental data. The guaranteed estimates of the γ0, generalized H2, and H∞ norms of a closed loop system and the corresponding suboptimal robust control laws are expressed in terms of solutions of linear matrix inequalities considering a priori knowledge and object modeling data. A numerical example demonstrates the improved quality of control systems when a priori and experimental data are used together. [ABSTRACT FROM AUTHOR]

As shown below, the linear operator norms in the deterministic and stochastic cases are optimal values of the Lagrange-dual problems. For linear time-varying systems on a finite horizon, the duality principle leads to stochastic interpretations of the generalized H2 and H∞ norms of the system. Stochastic minimax filtering and control problems with unknown covariance matrices of random factors are considered. Equations of generalized H∞-suboptimal controllers, filters, and identifiers are derived to achieve a trade-off between the error variance at the end of the observation interval and the sum of the error variances on the entire interval. [ABSTRACT FROM AUTHOR]

For linear dynamic plants, we consider a new class of controllers with adjustable parameters synthesized so as to reduce the integral indicators of the influence of initial and exogenous disturbances. The controller parameters are adjusted according to a differential equation in the direction of decrease of a local objective function. The conditions are stated under which the control objective is achieved, and the losses in comparison with time-invariant linear-quadratic and -optimal controllers are given, including the case of degenerate functionals. It is shown how these controllers are used in adaptive linear-quadratic and -optimal control for indeterminate plants whose parameters belong to a given polyhedron as well as in adaptive tracking of the reference model output. [ABSTRACT FROM AUTHOR]

For linear plants with unstructured or structured uncertainty of bounded norm, this paper designs Pareto optimal robust controllers in terms of linear matrix inequalities in multicriteria control problems with the generalized H2 or γ0 norms. The controller design procedure is based on optimization of a scalar objective function (Germeier convolution) and semi-definite programming. The developed theory is used to design multicriteria robust controllers in the stabilization problem for a rotor in electromagnetic bearings. [ABSTRACT FROM AUTHOR]

In the framework of the method of invariant ellipsoids, for a linear dynamic object a suboptimal linear dynamic controller by output is synthesized, at which the upper estimate of a maximum value of the norm of the controllable output reaches a minimum at all initial states of a system from a certain domain and at any disturbances bounded by the norm. [ABSTRACT FROM AUTHOR]

The need for a game-theoretical formulation of the problem of linear-quadratic control under nonmeasurable plant state where the functional depends on the uncertain initial state was substantiated. The minimax output control law in terms of linear matrix inequalities that may be regarded as the optimal robust control law for the given set of the plant initial states was established assuming that the measurable components of the initial state were known and the nonmeasurable components take on values within the given ellipsoid. The results obtained were generalized to the plants with uncertain parameters. [ABSTRACT FROM AUTHOR]

We consider the synthesis of linear control laws under one integral and several phase constraints on the basis of the Lyapunov function method and the technique of linear matrix inequalities. In particular, our method permits one to obtain suboptimal state or output feedbacks providing the minimum upper bound for a quadratic functional under phase and control constrains or the minimum bound for the maximum deviation of the controlled variable under one integral and several phase constraints. The synthesis is generalized to the case of nonstationary parametric perturbations in the plant. [ABSTRACT FROM AUTHOR]

We suggest a new method for solving the stabilization problem under phase constraints with the use of linear matrix inequalities. We consider the cases of complete and incomplete state measurements and the presence of nonstationary parametric perturbations. In the synthesis of linear control laws, the suggested method permits one to cover all possible quadratic Lyapunov functions and indicate a set of initial values for trajectories satisfying the phase constraints. [ABSTRACT FROM AUTHOR]

The article discusses the problem of constructing H1-controls and ensuring external perturbation breaking the dynamical systems described by the linear differential equations. The control has the feedback and is generated by the controller of a linear dynamical system of a given order whose input is fed with the measured output of the plant. The synthesis of H1-controllers suggested is based on the technique of linear matrix inequalities.

It is shown that the synthesis of robust H∞-control with respect to the output for systems with unknown limited parameters reduces to the solution of an optimization problem under constraints prescribed by a system of linear matrix inequalities. For this kind of problems, an optimization algorithm implemented with the use of standard procedures of the MATLAB package is suggested.The algorithm effectiveness is illustrated by the example of an optimal dampening of vibrations of a parametrically perturbed pendulum. [ABSTRACT FROM AUTHOR]

This article examines the necessary solvability conditions for Multiparameter Riccati Equations in the Robust Output Feedback H-Control Problem. It considers a controlled object that contains vectors of state, perturbation, control, controlled output, and measured output. The H-control problem for this object is the problem of constructing a dynamic measured-output feedback control law suppressing perturbations to a given ratio. Under specific system conditions, this problem has a solution if and only if the matrix algebraic Riccati equations have positive semidefinite stabilizing solutions.

The admissible value interval for the Lagrange multiplier in robust H∞ output control is shown to be finite. Its bounds are determined and a computation procedure is designed to estimate the minimal external perturbation suppression level that can be attained in an uncertain system with unknown bounded parameters by a dynamic output controller. [ABSTRACT FROM AUTHOR]

New parametric equations for H∞-controllers that suppress external perturbations in a given ratio for a linear dynamic object are derived. They do not contain the solutions of matrix equations or inequalities, but are parametrized by linearly contained parameters that take values in a domain defined by two frequency conditions. [ABSTRACT FROM AUTHOR]

We consider multicriteria minimax optimization problems with criteria in the form of the maxima of functionals given by the induced norms of linear operators taking the system inputs and/or initial state to the outputs. It is shown that replacing the difficult minimization of the linear convolution of such criteria by the minimization of the maximum of the linear convolution of the corresponding functionals leads to suboptimal solutions with an estimate of the degree of suboptimality with respect to Pareto optimal solutions. This approach is applied to Pareto suboptimal control design for linear finite-horizon time-varying and infinite-horizon time-invariant continuous- and discrete-time systems with uncertain initial states and/or disturbances. Numerical simulation results are presented. [ABSTRACT FROM AUTHOR]

It is demonstrated how to design optimal digital controllers on a finite horizon for the linear time-varying objects with uncertain initial conditions and external disturbances. The square of an optimality criterion, called the maximum output deviation, represents the exact guaranteed maximum value of the squared Euclidean norm of the system output normalized by the sum of the squared Euclidean norms of disturbances and a quadratic form of the initial state of a system. The maximum output deviations and the worst-case disturbances and/or initial conditions causing them, as well as the minimax controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) are calculated as solutions to a semidefinite programming problem. The necessary and sufficient conditions for the finite-time stability and boundedness of a system are established; they can be used for controller design. [ABSTRACT FROM AUTHOR]

We consider a linear time-varying system with an initial state and disturbance that are known imprecisely and satisfy a common constraint. The constraint is the sum of a quadratic form of the initial state and the time integral of a quadratic form of the disturbance, and these quadratic forms are allowed to be degenerate. We obtain a linear matrix differential Lyapunov equation describing the evolution of the ellipsoidal reachability set. In the problem of estimating the state based on output observations, this result is used to find the minimum-size ellipsoidal set of admissible system states, which is determined by the optimal observer and by the reachability set of the corresponding observation error equation. A method for control law synthesis ensuring that the system state reaches the target set or the system trajectory remains in a given ellipsoidal tube is proposed. Illustrative examples are given for the Mathieu equation, which describes parametric oscillations of a linear oscillator. [ABSTRACT FROM AUTHOR]

The maximum output deviation of a linear time-varying system is defined as the worst-case measure of the maximum value of the output Euclidean norm over a finite horizon provided that the sum of the squared energy of an external disturbance and a quadratic form of the initial state is 1. Maximum deviation is characterized in terms of solutions to differential matrix equations or inequalities. A modified concept of the boundedness of the system on a finite horizon under an external and initial disturbances is introduced and its connection with the concept of maximum deviation is established. Necessary and sufficient conditions for the boundedness of the system on a finite horizon are obtained. It is demonstrated that optimal controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) as well as controllers ensuring the boundedness of the system can be designed using linear matrix inequalities. [ABSTRACT FROM AUTHOR]