Showing papers on "Sliding mode control published in 1973"
TL;DR: In this paper, necessary and sufficient conditions for a system to be locally diffeomorphic to a linear system were derived, i.e., there exists a local diffeomorphism between the state spaces which carries a trajectory of the first system for each control into the trajectory of another system for the same control.
Abstract: Given two control systems where the control enters linearly, a necessary and sufficient condition is derived that these systems be locally diffeomorphic, i.e., that there exist a local diffeomorphism between the state spaces which carries a trajectory of the first system for each control into the trajectory of the second system for the same control. As a corollary we derive necessary and sufficient conditions for a system to be locally diffeomorphic to a linear system.
316 citations
139 citations
TL;DR: In this paper, the necessary conditions of optimal spatially independent control, spatially distributed control and boundary control of a class of counter-current distributed-parameter systems, the system dynamics of which are described by a hyperbolic system of first-order partial differential equations, are derived.
Abstract: By introducing a properly defined Hamiltonian and a Hamiltonian-like equation, the necessary conditions of optimal spatially independent control, spatially distributed control and boundary control of a class of counter-current distributed-parameter systems, the system dynamics of which are described by a hyperbolic system of first-order partial differential equations, are derived by calculus of variations. For a linear hyperbolic system with quadratic performance criterion to drive the system from one steady state to another a linear feedback control law is derived using the conjecture $
11 citations
01 Dec 1973
TL;DR: In this article, the problem of control of a stochastic system with control dependent noise is investigated, where both the system driving noise and the system measurement noise are assumed to have control dependent terms and the approximation of neglecting higher order terms in the control is introduced in the derivation of the a posteriori conditional covariance matrices of the system state.
Abstract: The problem of control of a stochastic system with control dependent noise is investigated. Both the system driving noise and system measurement noise are assumed to have control dependent terms. The approximation of neglecting higher order terms in the control is introduced in the derivation of the a posteriori conditional covariance matrices of the system state. These approximate conditional covariance matrices are used in a stochastic dynamic programming algorithm to obtain a linear feedback law. The control feedback matrices multiplying the estimates for system state are not those of the equivalent deterministic system and the separation theorem in its usual form does not apply to this class of problems. The control policy given by the algorithm reduces to the optimal control policy in two cases in which the optimal control is known. These are the case of no control dependent noise and the case of no measurement noise. A third order numerical example is investigated to illustrate the nature of the algorithm.
9 citations
01 Jun 1973
TL;DR: In this article, an analytical synthesis method for the feedback control of nonlinear multivariable systems was developed based on linearizing a system about a set of closely-spaced steady-state operating points and applying linear optimization methods at each point.
Abstract: : An analytical synthesis method for the feedback control of nonlinear multivariable systems was developed. The synthesis procedure derived is based on linearizing a system about a set of closely-spaced steady-state operating points and applying linear optimization methods at each point. A single nonlinear control problem is thereby reduced to a series of linear control problems. This permits the use of established analytical and numerical methods associated with linear optimal control theory. At each operating point, an optimal linear feedback controller is generated by minizing a quadratic performance criterion. Weighting factors within each performance criterion enable the control designer to satisfy performance specifications by trading-off system response against control actuation rates. Nonlinear feedback control is then constructed by combining the series of linear controllers into a single nonlinear controller whose feedback gains vary with system state. (Modified author abstract)
8 citations
01 Dec 1973
TL;DR: In this article, a method of equivalent control is proposed to derive the conditions for existence of sliding modes in variable structure systems with vector control inputs, where each component of the control vector is discontinuous on a corresponding surface in the system coordinate space.
Abstract: This paper treats variable structure systems with vector control inputs. Each component of the control vector is discontinuous on a corresponding surface in the system coordinate space. In such systems, sliding modes may arise and then trajectories lie on the discontinuity surfaces or their intersections. A so-called method of equivalent control is suggested which allows formal development of equations of such motions. The validity of the sliding mode equations derived through the equivalent control approach is established by introduction into the system of small nonidealities (of hysteresis, time-lag, and a periodic type) which are then made to tend to zero. It is suggested that Liapunov stability concepts be applied to derive the conditions for existence of sliding modes. It follows from the equations describing system evolution in the sliding mode that trajectory characteristics are dependent on the discontinuity surfaces equations. Therefore, proper selection of the surfaces on which the components of the control vector are discontinuous enables one to introduce desired properties into the system response. A desired response can be obtained if the trajectory reaches the intersection of the discontinuity surface starting from any initial state, and that at each point of the intersection the existence conditions for the sliding mode hold. The paper considers different methods of variable structure systems synthesis on the basis of the sliding modes being deliberately introduced into the system. Algorithms are described for controlling plants with both constant and variable parameters, and also plants with external disturbances. A class of systems is indicated in which evolution in the sliding mode possesses invariance with respect to variable parameters and disturbances.
4 citations
TL;DR: In this article, the gradient of a cost criterion has been found for a nonlinear dynamical system in the space of pulse-frequency modulated (PFM) control inputs, and the example presented shows that the gradient method gives the same numerical results as obtained through the use of the modified maximum principle.
Abstract: The gradient of a cost criterion has been found for a nonlinear dynamical system in the space of pulse-frequency modulated (PFM) control inputs The example presented shows that the gradient method gives the same numerical results as obtained through the use of the modified maximum principle
3 citations
01 Dec 1973
TL;DR: In this paper, the problem of optimal control of a nonlinear system with non quadratic final cost function admits a closed-loop suboptimal solution by approximation of the Lyapounov function by means of the control-equivalent Gaussian sum method.
Abstract: The problem of optimal control of a nonlinear system with non quadratic final cost function admits a closed-loop suboptimal solution by approximation of the Lyapounov function by means of the control-equivalent Gaussian sum method. Using the duality between optimal control for deterministic systems and estimation for stochastic systems, the solution is presented as the superposition of solutions of linear subsystems.
2 citations