Optimal Stabilization Problem Research Articles

Optimal synthesis in the problem of uniaxial stabilization for a satellite in the case of phase constraints

The optimal stabilization problem for the pitching oscillations of a satellite is considered. For the reduced system, an optimal control problem with phase constraints is formulated and a controllability domain is constructed. A necessary optimality condition (the maximum principle for the optimal control problem with phase constraints) is used to determine the optimal trajectories, the nature of interaction between a trajectory and the phase constraint boundary, and the number of boundary segments. An optimal synthesis is proposed in the constructed domain.

Problems of modeling and optimal stabilization of the gas-lift process

The problems of motion of fluids, gases and gas–liquid mixtures in pipes related to gas-lift oil recovery are mathematically formulated as systems of nonlinear hyperbolic partial differential equations. Optimal-control problems are posed based on the proposed models and some real assumptions. These problems can be used to design programmed paths and controls, which underlie the controllers that stabilize the pressure or volume of injected gas. That the mathematical models agree with available field and laboratory data is demonstrated by examples

Output-feedback Stabilization for Stochastic High-order Nonlinear Systems with a Ratio of Odd Integers Power

This paper investigates the problem of output-feedback control for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique, introducing a new rescaling transformation, and choosing an appropriate Lyapunov function, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. Furthermore, we address the problem of inverse optimal stabilization in probability. A simulation example is provided to show the effectiveness of the design.

State-feedback stabilization for stochastic high-order nonlinear systems with a ratio of odd integers power

This paper investigates the problem of globally asymptotically stable in probability by state-feedback for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique and choosing an appropriate Lyapunov function, a linear smooth state-feedback controller is explicitly constructed to render the system globally asymptotically stable in probability. Furthermore, we address the problem of state-feedback inverse optimal stabilization in probability. A simulation example is provided to show the effectiveness of the proposed approach.

ALGUNS ASPECTOS DO CONTROLE EM UM MODELO DINÂMICO DE OBJETOS DE PRODUÇÃO DE INTERAÇÕES CONFORME UMA FUNCIONAL QUADRÁTICA

Neste artigo são considerados dois tipos de controle em relação ao sistema de dois objetos de interação de produção, em que ura destes objetos produz uma mercadoria para aumentar os bens de capital e o outro produz um produto final, a fim de suprir a demanda dada. Inicialmente, determina-se o regime mais econômico de funcionamento do sistema, na condição de conservação da capacidade produtiva do mesmo durante longo tempo. Posteriormente, considera-se o problema de estabilização do desenvolvimento do sistema de objetos de produção em relação à trajetória programada de desenvolvimento. O segundo problema resolve-se através do método de programação dinâmica. Como funcional objetivo foi usada uma funcional quadrática, que admite desvios das coordenadas espaciais e funções de controle do regime programático.

Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable

After considering the stabilization of a class of high-order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control input, in this brief paper, we further address the problem of state-feedback inverse optimal stabilization in probability, i.e., our redesigned stabilizing backstepping controller is also optimal with respect to meaningful cost functionals.

Optimal State Feedback Input-Output Stabilization of Infinite-Dimensional Discrete Time-Invariant Linear Systems

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by state feedback. We show that a necessary and sucient condition for this problem to be solvable is that the transfer function has a right factorization over H-innity. A necessary and sucient condition in terms of an (arbitrary) realization is that each state which can be reached in a nite time from the zero initial state has a nite cost. Another equivalent condition is that the control Riccati equation has a solution (in general unbounded and even non densely dened). The optimal state feedback input-output stabilization problem can then be solved explicitly in terms of the smallest solution of this control Riccati equation. We further show that after renorming the state space in terms of the solution of the control Riccati equation, the closed-loop system is not only input-output stable, but also strongly internally stable.

Stabilization of linear autonomous systems of differential equations with distributed delay

Consideration is given to the problem of optimal stabilization of differential equation systems with distributed delay. The optimal stabilizing control is formed according to the principle of feedback. The formulation of the problem in the functional space of states is used. It was shown that coefficients of the optimal stabilizing control are defined by algebraic and functional-differential Riccati equations. To find solutions to Riccati equations, the method of successive approximations is used. The problem for this control law and performance criterion is to find coefficients of a differential equation system with distributed delay, for which the chosen control is a control of optimal stabilization. A class of control laws for which the posed problem admits an analytic solution is described.

On motion stabilization of nonstationary controlled system

In this paper, a solution to the problem of optimal motion stabilization of nonstationary controlled system basing on the constant-positive Lyapunov function is represented.

Nearly time optimal stabilizing patchy feedbacks

We consider the time optimal stabilization problem for a nonlinear control system x˙=f(x,u). Let T(y) be the minimum time needed to steer the system from the state y∊Rn to the origin, and call A(τ) the set of initial states that can be steered to the origin in time T(y)⩽τ. Given any ɛ>0, in this paper we construct a patchy feedback u=U(x) such that every solution of x˙=f(x,U(x)), x(0)=y∊A(τ) reaches an ɛ-neighborhood of the origin within time T(y)+ɛ.

Approximate optimal stabilization of solutions of a parabolic boundary-value problem by bounded control

For the problem of the optimal stabilization of a process described by a parabolic boundary-value problem, we construct and substantiate an approximate averaged feedback control (synthesis).

Optimal control of the rotational motion of a rigid body using moving masses

In this paper, the problem of optimal stabilization of a rotational motion of a rigid body around an axis fixed in the body with the help of internal moving masses is discussed using Lyapunov function technique. The control forces leading to the rotational motion are derived. The optimal control forces ensuring the asymptotic stability of this motion are derived. Some of special cases of the investigated problem are considered. Moreover, some of the results are compared with those obtained in literature by other methods.

Optimal stabilization of a rigid body motion using rotors system

In this paper, the problem of optimal stabilization of an angular motion of a rigid body, with the help of internal rotors, is investigated using the Lyapunov–Bellman technique. The conditions of optimal stabilization of this motion are adopted to obtain the control law as functions of the phase coordinates of the system and time. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by Euler’s equations. Moreover, some of the results are compared with those obtained in other literatures.

Polynomial H2-Optimization of Sampled-Data Ship Control Systems in Continuous Time

The problem of optimal digital ship course stabilization under stationary stochastic disturbances is considered. The chosen cost function consists of a weighted sum of average (with respect to continuous time) variances of the controlled variable (yaw angle) and control signal (rudder angle). A polynomial design method is developed on the basis of the parametric transfer functions method for direct design of optimal digital controller.

Optimal stabilization of the equilibrium positions of a rigid body using rotors

In this work, the problem of optimal stabilization of the equilibrium positions of a rigid body using internal rotors is studied. The conditions for the optimal stabilization of the equilibrium positions are used to deduce a feedback control law as functions of the phase coordinates of the body and the parameters describing the equilibrium positions. The Lyapunov function is used to prove the asymptotic stability of these positions. Special cases and analysis of the obtained results are presented to assess the present method. Moreover, some of the results are compared with those obtained in the literature using other methods. In contrast to the usual methods in the literature, which stabilize some of the equilibrium positions of the rigid body, the present one has the advantage of stabilizing all the equilibrium positions with optimal control law.

Inverse optimal stabilization for feedforward nonlinear systems

In this paper is solved the inverse optimal stabilization problem for nonlinear nonaffine control discrete-time systems which are globally stable when uncontrolled. Stabilizing feedback laws and cost functionals are given by explicit formulas. We apply the result to feedforward systems.

On the passive stabilization of the equilibrium state of Lagrangian systems

The idea of passive stabilization of a dynamical system whose motion is not asymptotically stable was advanced for the first time in the monograph [1] by introducing supplementary degrees of freedom. Based on this idea, Savchenko [2] discussed the stabilization of Hamiltonian systems by a nonlinear method (namely the method of passive stabilization by defreezing parameters). The authors of this paper investigate the effectiveness of its application to a Lagrangian system by a mechanical model which has independent scientific meaning. A comparison is also made between this model and another similar mechanical model. The problem of optimal passive stabilization is solved at the end of the paper. It is shown that this problem is closely connected with the resonance situations.

Bezout factors and L/sup 1/-optimal controllers for delay systems using a two-parameter compensator scheme

The authors consider the simultaneous problem of optimal robust stabilization and optimal tracking for single-input/single-output (SISO) systems in an L/sup /spl infin//-setting using a two-parameter compensator scheme. Optimal robustness is linked to the work done by Georgiou and Smith (1992) in the L/sup 2/-setting. Optimal tracking involves the resolution of L/sup 1/-optimization problems. The authors consider in particular the robust control of delay systems. They determine explicit expressions of the Bezout factors for general delay systems which are in the Callier-Desoer class /spl Bscr//spl circ/(0). Finally, they solve several general L/sup 1/-optimization problems and give an algorithm to solve the optimal robust control problem for a large class of delay systems.

Optimal control over evolution stochastic systems and its application to stochastic models of financial mathematics

We consider problems of optimal stabilization of controlled evolution stochastic systems in semi-Markov media and their application to financial stochastic models.

The stabilization of controlled systems with a guaranteed estimate of the control quality

The problem of stabilizing motion in controlled systems with a guaranteed estimate of the control quality is considered. It arises from the optimal stabilization problem when the conditions on the cost functional are relaxed: no minimization of this functional is required, it is only necessary for it not to exceed a certain limit. This enables the class of solvable problems to be extended compared to the class of optimal stabilization problems. The solution of the problem is based on Lyapunov's direct method using Lyapunov functions with derivatives of constant sign. Some of the results are new even in the case of the optimal stabilization problem. The following examples are considered: a holonomic mechanical system with time-dependent Lagrangian, a controlled linear mechanical system and the problem of using the gravitational moment to stabilize the controlled plane rotational motion of a satellite in an elliptic orbit.