Showing papers on "Separation principle published in 1989"
TL;DR: In this paper, a robust controller including a new type of observer called the proportional integral observer (PI observer) is proposed, which differs from the conventional one by an integration path which provides additional degrees of freedom.
Abstract: A design method for a robust controller including a new type of observer called the proportional integral observer (PI observer) is proposed. The new observer differs from the conventional one by an integration path which provides additional degrees of freedom. This freedom can be used to make the observer-based controller design less sensitive to parameter variation of the system. It is shown that some of the difficulties that may arise in the exclusive pursuit of a design for the conventional observer-based controller from the point of view of system robustness are resolved in a straightforward manner using the PI observer. A systematic robustness recovery procedure is described for the PI observer-based controller design which asymptotically achieves the same loop transfer functions as the full-state feedback control implementation. A design example is included and the effectiveness of our method is illustrated by simulation results.
158 citations
13 Dec 1989
TL;DR: In this article, the Luenberger observer is used in the state estimation of the extended nonlinear system, and the use of high gains in the cancellation of nonlinearities in order to simplify the observer design is studied.
Abstract: The estimation of the unknown parameters of a nonlinear system is reduced to the estimation of its state variables by a state-space immersion. The Luenberger observer is used in the state estimation of the extended nonlinear system. The use of high gains in the cancellation of nonlinearities in order to simplify the observer design is studied. The high gain induces a time-scale separation between the nonlinear system and the observer, and therefore the singular perturbation theory can be used in the stability analysis of the error dynamics. In particular, it is shown that the error dynamics reaches stable equilibrium very fast, ensuring that the slow dynamics of the observer is just that of the given nonlinear system. >
110 citations
Book•
14 Sep 1989TL;DR: In this paper, a formal approach to optimal filtering and control of distributed parameter systems is presented. But it does not address the problem of finding the optimal filter for a distributed parameter system.
Abstract: Part 1 Mathematical theory: some basic results in the theory of partial differential equations - Bellman-Gronwall inequality, Sobolev spaces, Green's formula stochastic partial differential equations - radon measures, cylindrical probability, Gaussian cylindrical probability, nuclear and Hilbert-Schmidt operators, conditional expectation, Hilbert- space-valued Wiener processes optimal control of deterministic distributed parameter systems - elliptic systems, the Dirichlet problem, the Neumann problem, parabolic systems, Riccati equation, Hamilton-Jacobi equation, hyperbolic systems controllability and observability linear estimation theory - finite-dimensional estimation theory, estimation for random linear functionals optimal filter for distributed parameter systems - the filtering problems, Wiener filter, Kalman-Bucy filter, recursive formula for the optimal filter, innovation theory, duality between estimation and control, optimal filter for hyperbolic systems stochastic optimal control of distributed parameter systems formulation of the model, the stochastic optimal control problem, necessary and sufficient conditions for optimality, the separation principle identification of distributed parameter systems - the basic concept of system identification, modal approximation for identification, regularization. Part 2 Engineering Applications: formal approach to optimal filtering and control of distributed parameter systems - Wiener-Hopf theorem, the optimal filter, predictor and smoothing estimator, various approaches to linear estimation problems stochastic optimal control problems optimal sensor and actuator location problems - optimal sensor location problems, optimal actuator locations computational techniques for identification of distributed parameter systems - stochastic approximation, least squares identification, the Galerkin finite-element model, discrete regularization and minimization.
110 citations
TL;DR: In this paper, the effects of observer motion on estimation accuracy for bearings-only localization were investigated. But the observer motion involves a trade-off between increasing bearing-rate and decreasing range.
Abstract: System observability in nonlinear estimation problems is a significant factor governing solution behavior. This paper addresses the effects of observer motion on estimation accuracy for bearings-only localization. The role of the observer is to create a target/observer geometry that maximizes system observability, thereby minimizing the region of uncertainty. Two approaches are presented for deriving optimal observer paths. The first approach generates optimal observer motion numerically via the determinant of the Fisher Information Matrix, while the second involves the application of control theory to an alternative criterion. In addition, optimal fixed aspect angles are similarly determined for deviated pursuit curves. The error ellipses associated with the trajectories are compared and analyzed. It is shown that observer motion involves a trade-off between increasing bearing-rate and decreasing range. Particular characteristics of an observer path and its effect on estimation accuracy depend on the scenario initially encountered.
88 citations
TL;DR: In this paper, a full state vector observer is derived for a class of linear differential state delayed control systems, which can be designed by well-known finite-dimensional state vector methods once the set of unstable and poorly damped modes of the system has been determined.
Abstract: A full state vector observer is derived for a class of linear differential state delayed control systems. The approach dualizes a feedback stabilization theory based on the reducing transformation technique. A major feature of the approach is that the observer, or the combined controller/observer, can be designed by well-known finite-dimensional state vector methods once the set of unstable and poorly damped modes of the system has been determined. >
78 citations
06 Nov 1989
TL;DR: In this article, a robust control technique for robotic motion is developed, in which the feed forward loop compensates the interactive torque, which the observer identifies with a certain time delay, if the time delay of the observer is negligibly small, an acceleration controller is realized.
Abstract: An analysis of robustness and a design principle for advanced motion control in robotics are presented. The performance of motion control in a single joint is evaluated according to its robustness. A robust control technique for robotic motion is developed. For quick recovery, the feedforward loop compensates the interactive torque, which the observer identifies with a certain time delay. If the time delay of the observer is negligibly small, an acceleration controller is realized. In the observer-based system, it is possible to show that this delay also determines the sensitivity function, which is the index of how the controller reduces the effect of not only the interactive torque but also the parameter variations. In a multi-degree-of-freedom motion system, the total mechanical system is described by the dynamical equations and the kinematic equations. If a drive system in each joint is an observer-based acceleration controller, only the kinematics need be taken into account in the motion control. Several examples in robotics of motion systems applied to position control and force control systems are discussed. >
65 citations
13 Dec 1989
TL;DR: In this article, necessary and sufficient conditions for the solution of a general nonlinear output regulation problem are given, and the connection between the problem in question and appropriate nonlinear versions of the concept of steady-state response and of the separation principle is established.
Abstract: Necessary and sufficient conditions are given for the solution of a general nonlinear output regulation problem. The proof of this result illustrates the connection between the problem in question and appropriate nonlinear versions of the concept of steady-state response and of the separation principle. >
57 citations
21 Jun 1989
TL;DR: In this article, the problem of observer design for a class of state-feedback controllers that includes high-gain linear control, continuous approximations of min-max control and variable structure control is studied.
Abstract: In this paper we study the problem of observer design for a class of state-feedback controllers that includes high-gain linear control, continuous approximations of min-max control and continuous approximations of variable structure control. Assuming that the state-feedback controller robustly stabilizes the system in the presence of matched parametric uncertainties, we are to design the observer such that the observer-based control recovers the stability robustness of the state-feedback-control. We will show that it is possible to design such an observer, if the nominal, system is left-invertible and minimum-phase.
37 citations
TL;DR: The problem of pole assignment and asymptotic observer design for multi-input multi-output continuous descriptor (generalized state-space) systems is studied and the extension of the separation principle to descriptor systems is given.
Abstract: The problem of pole assignment and asymptotic observer design for multi-input multi-output continuous descriptor (generalized state-space) systems is studied. The problem is solved by introducing a new canonical form for controllable descriptor systems. The internal stability of the descriptor variable feedback and observer configuration is also considered, i.e. the extension of the separation principle to descriptor systems is given.
22 citations
TL;DR: In this article, it is shown that, under a suitable assumption involving the reachability set, the optimal control exists and is unique, and both open-loop and feedback descriptions of the optimal controller are given.
Abstract: This paper deals with the linear-quadratic control problem (LQCP) with a fixed terminal state, for infinite-dimensional systems defined by evolution operators. It is shown that, under a suitable assumption involving the reachability set, the optimal control exists and is unique. To solve the problem effectively, its connection with the minimum-energy control for the perturbed system is exploited. Both open-loop and feedback descriptions of the optimal control are given. Important relationships between the controllability of the system and properties of the optimal control are described, and a feedback approximation to the optimal control is given.
18 citations
TL;DR: A new method is presented where the observer equations are augmented to include a first-order filter dynamics, resulting in no perturbation of controlled system eigenvalue locations.
Abstract: Modern modal control methods for flexible structures have control and observation spillover that can degrade performance and reduce the stability margin of the closed-loop controlled structure. The sensor output is often filtered to reduce observation spillover, however, the filter introduces signal distortion and perturbs the closed-loop system eigenvalue locations. This perturbation can reduce the stability margin and jeopardize convergence of a deterministic observer. If the filter equations are not explicitly included in the observer design, then the separation principle between the controller and the observer states no longer holds when present in the unfiltered system. A new method is presented where the observer equations are augmented to include a first-order filter dynamics. The separation principle, controllability, and observability of the unfiltered system are invariant to the filter dynamics in this new method, resulting in no perturbation of controlled system eigenvalue locations. The filter cutoff frequency can be located even within the bandwidth of the system, thereby increasing the filter effectiveness in reducing observation spillover. Spillover-generated errors in closed-loop eigenvalues of these control methods are compared using a numerical example.
13 Dec 1989
TL;DR: In this article, the LQG (linear quadratic Gaussian) control problem is formulated and solved for multivariable systems where the output variables of the plant are measured at different rates.
Abstract: The LQG (linear quadratic Gaussian) control problem is formulated and solved for multivariable systems where the output variables of the plant are measured at different rates. These rates can be definitively less than the unique rate adopted for input updating. It is shown how a suitable description of both the plant and the skew sampling mechanism can be given in terms of a linear periodic system. Then the solution is worked out by solving a singular periodic prediction problem and by resorting to the separation principle. >
TL;DR: In this article, strong variations for the ϵ-optimal control of a class of control problems for systems described by stochastic diffusion equations are described, and the differentiation process developed identifies the adjoint process.
TL;DR: In this article, the exact penalty function method was used to transform a constrained optimal control problem into an unconstrained control problem, which can be easily solved by a numerical technique.
Abstract: Given the well known concept that optimal control problems may be solved either by the maximum principle or by the dynamic programming technique which employs many numerical algorithms, this paper attempts to show that the exact penalty function method may be used to transform a constrained optimal control problem into an unconstrained optimal control problem. Under certain conditions the constrained optimal control problem is shown to be equivalent to an unconstrained optimal control problem, which can be easily solved by a numerical technique.
TL;DR: In this article, a multiple controller structure consisting of a typical feedback controller and an additive redundant controller is proposed for enhancing the reliability of the control system, which ensures the performance of tracking a given set-point input under failure in one of controllers or parameter perturbations of the plant.
Abstract: A multiple controller structure consisting of a typical feedback controller and an additive redundant controller is proposed for enhancing the reliability of the control system. This scheme ensures the performance of tracking a given set-point input under failure in one of controllers or parameter perturbations of the plant. Dynamic reliability for the double control system is formulated in terms of the mean time to failure (MTTF) and asymptotic convergence of the tracking error to zero is shown. For the case in which the main controller is chosen as the optimal set-point tracking controller and the redundant controller as the model-reference adaptive controller (MRAC) whose reference model is the closed-loop combination of the plant and the main controller, it is proven that the control system is more reliable than the system with only the single main controller in the sense of extended dynamic reliability, and further reliable operation of the control system is illustrated by numerical examples when the...
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01 Jan 1989
TL;DR: In this paper, it was shown that an estimate of the states x can be obtained using an asymptotic observer whenever the system is observable, and that an observer of order (n-m) is adequate to estimate all the states.
Abstract: This chapter shows that an estimate of the states x can be obtained using an asymptotic observer whenever the system is observable. We also showed that an observer of order (n-m) is adequate to estimate all the states. We also defined a minimal order observer to estimate linear functions of states. When only a single (scalar) linear function of states is desired, an observer of order (r-1), where r is the observability index of the system, is possible.
TL;DR: In this article, a new formulation is presented for a class of partially observed linear stochastic control problems described by three sets of stochaslic differential expressions: one for the system to be controlled, another for the observer (measurement) channel and the control channel driven by the observed process.
Abstract: A new formulation is presented for a class of partially observed linear stochastic control problems described by three sets of stochaslic differential expressions: one for the system to be controlled, one for the observer (measurement) channel and one for the control channel driven by the observed process. The noise processes perturbing the system and observer dynamics are vector-valued counting processes (in particular Poisson processes) with time varying intensities. The approach is constructive, determining the optimal linear feedback control law subject to constraints on control (gain) matrices and closed loop system uncertainly. This makes the approach directly appealing to control system design. For illustration, numerical examples are solved using the proposed approach.
TL;DR: In this article, a new control scheme with an optimal observer is presented for optimal control of civil engineering structures, where the purpose is to increase the reliability and robustness of the control system.
Abstract: A new control scheme with an optimal observer is presented for optimal control of civil engineering structures. The purpose is to increase the reliability and robustness of the control system. In classical optimal control without observer, there is no relationship between the real and simulated vibrations of structures. Thus, if any discrepancy occurred between the two, vibration might be amplified rather than controlled. Due to regulator‐observer control in the proposed optimal feedback control scheme, stable control is achieved very quickly in an asymptotic manner. The following conclusions are obtained. It is preferable to use the optimal regulator control because of its simplicity. It can be shown numerically that the same degree of control can be achieved using optimal regulator control as is achieved using optimal m‐step control. Further, it is preferable to use the optimal observer because the structure can be controlled steadily even if there is a discrepancy between real and simulated vibrations....
TL;DR: In this article, a reduced-order time-varying state observer for voltage and current-fed induction motor is presented, and the observer error decreasing rate is arbitrarily formed by a suitable choice of the observer eigenvalues, which does not depend on the rotor speed.
Abstract: In this paper a new type of the reduced-order time-varying state observer for voltage- and current-fed induction motor is presented. The observer error decreasing rate is arbitrarily formed by a suitable choice of the observer eigenvalues, which does not depend on the rotor speed. Stability of the observer is proved. Dynamical properties of such observers in various operating conditions of the drive system are analysed. Results are numerically verified by simulation.
TL;DR: A separation principle is developed, which indicates that one can estimate multichannel Gaussian amplitudes and Bernoulli events separately, and approaches for estimation of these quantities are discussed.
Abstract: General problems and solutions are described for maximum a posteriori estimation of multichannel Bernoulli-Gaussian sequences, which are inputs to a linear discrete-time multivariable system. The authors first develop a separation principle, which indicates that one can estimate multichannel Gaussian amplitudes and Bernoulli events separately. They then discuss approaches for estimation of these quantities. >
TL;DR: In this article, an explicit construction of the ∈-optimal control in a separated form is given, and it is shown that the infimum of the expected cost over the set of separated controls is the same as the ∆-optimality of a set of admissible controls, which depend non anticipatively on the observation process.
Abstract: The stochastic control problem of partially observed systems is approximated by a sequence of partially observed impulse control problems with non-zero but vanishing impulse costs. For the latter problems, we give an explicit construction of the so-called ∈-optimal controls in a separated form.As a consequence of this approach, we prove that the infimum of the expected cost over the set of separated controls-i.e. which depend non anticipatively on the filtering process-is equal to the infimum of the expected cost over the set of admissible controls-i.e. which depend non anticipatively on the observation process.For the classical situation of linear systems, this method yields the existence of an optimal separated control.
03 Apr 1989
TL;DR: It is proved in this paper that this method can be formulated to minimize the observer gain to the system input and is a deterministic approach of the recovery, of loop transfer function and robustness of direct state feedback system.
Abstract: This paper shows that based on the recent development of observer design solution, an observer pole selection method can be formulated to minimize the observer gain to the system input. It is proved in this paper that this method is a deterministic approach of the recovery, of loop transfer function and robustness of direct state feedback system.
TL;DR: In this paper, a new method is proposed for solving the linear-quadratic problem of optimal control for a partially observable stochastic Volterra process, which relies on the representation and optimal estimation of the optimal control in the form of integrals over the observable process.
01 Oct 1989
TL;DR: An optimal state-feedback control law is developed to achieve fast and stable speed regulation with minimum control effort, based on optimal multivariable system theory.
Abstract: The authors present a design approach for the control of DC motors, based on optimal multivariable system theory. An optimal state-feedback control law is developed to achieve fast and stable speed regulation with minimum control effort. The basic feature of the system is the fast and accurate estimation of either the rotor speed or the armature current, using an optimal reduced-order observer. An application example and some digital simulation results, indicating the effectiveness of the system, are presented. >
TL;DR: In this article, a microcomputer-based implementation of an optimal stochastic regulator for a feeding process is presented, where the regulator design can be interpreted as a problem of linear optimal signal estimation.
21 Jun 1989
TL;DR: In this article, an optimal observer-based control law derived using both pole-placement techniques and optimal linear regulator theory is proposed to estimate the unknown force input and provide excellent noise rejection, at the expense of significantly slower transient response.
Abstract: A two-axis skin friction balance developed at the Langley Research Center employs a state-variable feedback nulling circuit developed via multivariable pole-placement theory. Because of the inherently noisy wind tunnel environment where the balance operates, a less noise-sensitive controller is needed. This paper investigates the application of optimal-observer-based control laws derived using both pole-placement techniques and optimal linear regulator theory. Although a pole-placement-derived control law with optimal observer provides fast response and excellent noise rejection, its observer requires an electrical input proportional to the unknown skin friction force, which is unavailable. To overcome this limitation, an optimal linear regulator design is proposed which estimates the unknown force input and provides excellent noise rejection, at the expense, however, of significantly slower transient response.
13 Dec 1989
TL;DR: The author shows how to use partial differential equation techniques to simplify the proofs as much as possible and to permit more general classes of approximate feedback to be envisioned.
Abstract: Finite-dimensional filters are used in the context of stochastic control with partial information to obtain a kind of approximate separation principle. It turns out that many technical problems are met in the study of the approximation and that some simplification is desirable. The author shows how to use partial differential equation techniques to simplify the proofs as much as possible and to permit more general classes of approximate feedback to be envisioned. >