Showing papers on "Separation principle published in 1981"
TL;DR: In this paper, the stochastic maximum principle is applied to solve eight different control problems with special structure and the main thrust of the work is to show that some completely observable control problems can be solved quite quickly and easily using the maximum principle.
Abstract: The stochastic maximum principle is applied to solve eight stochastic control problems. Four have been solved previously using much more complicated methods, but the last four are new. The main thrust of the work is to show that some completely observable stochastic control problems with special structure can be solved quite quickly and easily using the maximum principle.
49 citations
01 Dec 1981
TL;DR: In this paper, a new low sensitivity realization for the quadratic regulator is derived, based on a generalization of the balanced realizations of Moore via the separation principle, which leads directly to a new approximation method for the LQG problem and reduced order regulator synthesis.
Abstract: A new low sensitivity realization for the quadratic regulator is derived. The main idea is the generalization of the "balanced realizations" of Moore via the separation principle. The results lead directly to a new approximation method for the LQG problem and reduced order regulator synthesis.
41 citations
TL;DR: In this paper, a method for the design of an observer capable of reconstructing a single linear functional of the states of a linear finite-dimensional system is presented, subject to the restriction that the observer eigenvalues be freely assignable.
Abstract: This paper presents a method for the design of an observer capable of reconstructing a single linear functional of the states of a linear finite-dimensional system. The goal of this method is the design of an observer having minimum order subject to the restriction that the observer eigenvalues be freely assignable. The method avoids using involved canonic forms for the given system.
33 citations
TL;DR: In this article, a minimum principle for stochastic control problems with output feedback was derived by applying Bismut's minimum principle to the Kushner-Stratonovitch equation describing the controlled evolution of the conditional density of the state.
20 citations
TL;DR: Bellman's principle of optimality and dynamic programming are shown to be the basis for solution of a physically significant class of nonlinear stochastic control problems as discussed by the authors, and a new result which extends the separation principle is presented.
Abstract: Bellman's principle of optimality and dynamic programming are shown to be the basis for solution of a physically significant class of nonlinear stochastic control problems. Various previous results are integrated into a survey here, and a new result which extends the separation principle is presented. Certain bilinear and linear-in-control systems are included in the analysis.
14 citations
01 Jan 1981
TL;DR: In this paper, the role of the morphism in unity feedback synthesis (UFS) is investigated, and it is shown that this morphism can be used to improve the performance of UFS.
Abstract: Under broad assumptions, it is known [1] that there is, in general, no "separation principle" to guarantee optimality of a division between control law design and filtering of plant uncertainty. It is possible, however, to develop parameterizations of nominal responses and to examine their capabilities in the feedback situation. In an earlier study, the authors presented a coordinate-free approach [34] to the Nominal Design Problem (NDP), which addresses control action and plant output syntheses, independently of the controller configuration. It was shown that NDP depended only upon plant structural matrices and a single design morphism. This paper studies the role of this design morphism in unity feedback synthesis (UFS). NDP, together with feedback synthesis, is understood as a Total Synthesis Problem.
13 citations
01 Mar 1981
TL;DR: In this paper, the combined problem of optimal impulse control and filtering, for a stochastic linear dynamic system observed via a noisy linear channel, was shown to be reduced to two independent problems, i.e., the problem of filtering and impulse control, respectively.
Abstract: In this paper, one shows that the combined problem of optimal impulse control and filtering, for a stochastic linear dynamic system observed via a noisy linear channel, can be reduced to two independent problems of impulse control and filtering, respectively.
13 citations
TL;DR: In this article, a method using the necessary conditions for optimality of the first and second order of the type considered in Pontryagin's maximum principle was proposed, and the convergence of the method was proved.
Abstract: OPTIMAL control problems with free right-hand end may be solved by a method using the necessary conditions for optimality of the first and second order of the type considered in Pontryagin's maximum principle. The convergence of the method is proved, computational aspects are discussed, and the effectiveness of the method is illustrated by examples.
10 citations
TL;DR: In this article, the optimal control of time-varying distributed parameter systems in a Banaoh space is studied and the reachable region of the system is proved to be a convex set even when the control domain is not convex.
7 citations
TL;DR: In this article, the optimal control law for a linear system and a quadratic performance index is given by state feedback, and the main purpose of this paper is to obtain necessary and sufficient conditions for the optimality to hold irrespectively of the choice of observer.
Abstract: The optimal control law for a linear system and a quadratic performance index is, as is well known, given by state feedback. In the case where there exist some inaccessible state variables, and where an observer is incorporated in a feedback loop to estimate them, the resultant control law is no longer optimal almost always for the original performance index. In the present paper we discuss whether or not it is optimal for some quadratic performance index. More precisely, we study the optimality of an optimal feedback control law incorporating the observer, in the sense that it minimizes some quadratic performance index for the system augmented by the observer. The main purpose of this paper is to obtain necessary and sufficient conditions for the optimality to hold irrespectively of the choice of observer.
6 citations
TL;DR: In this paper, the design and implementation of a controller to stabilize a single-input single-output (SISO) unstable plant using pole-assignment technique and observer theory is considered.
Abstract: This paper considers the design and implementation of a controller to stabilize a single-input single-output unstable plant using pole-assignment technique and observer theory. First, assuming that the state variables are available for feedback, the pole-assignment technique is used to determine the feedback gains required to achieve a desired set of closed-loop poles. This assumption is relaxed and an observer is designed to estimate the control law using output feedback. The unstable plant is simulated on a TR48 analog computer with the controller in the feedback loop. Active network implementation of the controller is discussed.
TL;DR: In this paper, the problem of designing an optimal partial state observer which minimizes the increase in the cost performance for the usual regulator problem is considered, and the optimal criterion is generalized and is the time integral of the mean square estimator error.
Abstract: This paper considers the problem of designing an optimal partial state observer which minimizes the increase in the cost performance for the usual regulator problem, The optimal criterion is generalized and is the time integral of the mean square estimator error. It is assumed that the initial system state is an unknown random vector with known mean and covariance. The necessary conditions for this optimality are derived when the subspace, for which a partial state observer could be constructed, is given. Also, a design algorithm is obtained which can be directly solved for the parameters of the optimal observer and requires the solution of a matrix Riccati equation of the observer order. It is also shown that the separation property in the restricted sense does apply in this problem. Moreover the effectiveness of the partial state observer is compared with that of the complete state observer. Finally a simple example is presented to illustrate the procedure.
TL;DR: In this article, a method is presented for exactly reconstructing the complete state variables from observed state variables, and it is believed that this is the first time that such a method has been used for exact reconstructing state variables.
TL;DR: In this article, the optimal control of traffic flow on a two-lane highway, in the macroscopic, and thus deterministic, theory, is studied, where the state of the system is expanded as a series of complete orthogonal functions and in this way the initial linear distributed system is converted into an infinite-dimensional linear system with lumped parameter.
Abstract: This paper deals with the optimum control of traffic flow on a two-lane highway, in the macroscopic, and thus deterministic, theory. For the ease of the reader, the nonlinear partial differential equations of the system are first straightforwardly derived from the well-known equation of conservation of vehicles. Then the system is linearized around a nominal trajectory and the problem is defined as the optimum control of the deviation of the system from this nominal state. To Bolve this problem the state of the system is expanded as a series of complete orthogonal function, and in this way the initial linear distributed system is converted into an infinite-dimensional linear system with lumped parameter. A 2N-order truncated version is considered (therefore the sub-optimal approach) and the theory of the observer is applied when the number of available observation measurements is less than the order of the system. Considerations on the practical implementation of the control system are given.
01 Dec 1981
TL;DR: In this article, the authors considered the linear quadratic regulator problem for a class of linear, randomly varying systems based on partial observation, where the state estimator is non-linear and the separation principle does not hold.
Abstract: In this paper we consider the linear quadratic regulator problem for a class of linear, randomly varying systems based on partial observation. The novelty, in part, of the solution is that the state estimator is non-linear and the separation principle does not hold (not in the usual sense, at any rate). Using a linear approximation, we indicate a procedure for constructing a class of approximately optimal controls.
TL;DR: In this article, a formula for the closed-loop root locus of a linear control system, designed using the separation principle, when the loop gain is changed from its nominal value is given, and extensions to dynamic mismatch, discrete time systems, and reduced-order dynamics are discussed.
Abstract: A formula is given for the closed-loop root locus of a linear control system, designed using the separation principle, when the loop gain is changed from its nominal value. An illustrative example is given, and extensions to dynamic mismatch, discrete-time systems, and reduced-order dynamics are discussed.
TL;DR: In this paper, a non-linear stochastic system, representing a jump-diffusion process, and also a measurement process representing a nonlinear, and noisy observation of the state are given.
Abstract: A non-linear stochastic system, representing a jump-diffusion process, and also a measurement process representing a non-linear, and noisy observation of the state are given. A dynamic state observer i3 introduced, and the control vector is designed to be a function of the output of the state observer. The designer has to choose a pair (v, G), where v is the control vector and Q a gain matrix of the state observer, both v and Q being functions of the output of the state observer, and such that a given performance index will be minimized. By applying the calculus of variations, necessary conditions on an optimal pair (v0, G0) are derived, these conditions being given by a pair of coupled non-linear partial integro-differential equations. Finally, an example is solved numerically.
TL;DR: In this paper, a controller and an observer with some optimality for the model is constructed and its robustness is shown, and the relation between the original disturbance and the state vector of the observer is considered.
TL;DR: In this article, an improved optimal regulator control system synthesis method is presented for step, ramp and sinusoidal desired signals and step change of the load, where the configuration of the controller is compared with that of the PID controller.
Abstract: To reveal the effectiveness of an improved optimal regulator control system synthesis method which has been developed in a previous paper, experimental studies have been carried out using the usual microprocessor system. Experimental results of the control system are presented for step, ramp and sinusoidal desired signals and step change of the load. Zero steady-state errors are obtained for all the cases. while the steady-state error of the control system with a PID controller is not necessarily zero for non-step functions of the desired signals. The configuration of the controller is compared with that of the PID controller. This controller includes proportional action, a kind of derivative action and integral action : however, the function of each action is not necessarily the same as that of the PID controller.
01 Dec 1981
TL;DR: In this paper, the problem of designing an optimal partial state observer which minimizes the increase in the cost functional for the usual regulator is considered, and a design algorithm is obtained which can be directly solved for the parameters of the optimal observer, and requires the solution of a Riccati equation of observer order.
Abstract: This paper considers the problem of designing an optimal partial state observer which minimizes the increase in the cost functional for the usual regulator. It is assumed that the initial system state is an unknown random vector with known mean and covariance. The necessary and sufficient conditions for this optimality are derived when the subspace, for which a partial state observer could be constructed, is given. And a design algorithm is obtained which can be directly solved for the parameters of the optimal observer, and requires the solution of a Riccati equation of observer order. It is also shown that the separation property in the restricted sense does apply in this problem.
TL;DR: In this article, the stability of the overall closed-loop system composed of an originally unstable nonlinear system, a state observer and a linear gain state feedback controller is investigated, and it is shown that for certain classes of nonlinear systems, even a linear identity observer can be used to provide global asymptotic stability.
TL;DR: In this paper, a method to synthesize a feedforward control and a reduced order feedback compensator which is expected to be low sensitive to parameter variations are presented under the condition that the optimal state feedback regulator is already synthesized.
TL;DR: In this article, a necessary and sufficient characterization condition for good approximations in arbitrary subsets of the Hahn-Banach extension theorem is given. But this condition is a generalization of the so-called Global Kolmogoroff condition.
Abstract: Most results of best approximation theory are known to be intimately related to various forms of the Hahn-Banach extension theorem. The present paper attempts to highlight: how an elementary geometrical separation principle pervades much of the good and best approximation theory, by showing how all characterizations old and new are indeed potential variants of this principle. The main result consists in a necessary and sufficient characterization condition for good approximations in arbitrary subsets. Moreover a striking result is obtained simply by particularizing this main theorem to best nonlinear approximation theory. Indeed a necessary and sufficient characterization condition is formulated which is shown to be a generalization of the so-called Global Kolmogoroff condition.
TL;DR: In this paper, a non-classical structure of incomplete information in N-person non-cooperative differential games, team problems and stochastic control is studied, where the noisy observations available to the decision makers are instantaneous and memoryless.
01 Dec 1981
TL;DR: A method for designing observers which utilizes state disturbance information is given and this approach is a natural dual to the control eigenvalue/eigenvector placement design.
Abstract: A method for designing observers which utilizes state disturbance information is given. This approach is a natural dual to the control eigenvalue/eigenvector placement design.