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1.
It is shown that H ∞ optimization is equivalent to weighted H 2 optimization in the sense that the solution of the latter problem also solves the former. The weighting rational matrix that achieves this equivalence is explicitly computed in terms of a state-space realization. The authors do not suggest transforming H ∞ optimization problems to H 2 optimization problems as a computational approach. Rather, their results reveal an interesting connection between H ∞ and H 2 optimization problems which is expected to offer additional insight. For example, H 2 optimal controllers are known to have an optimal observer-full state feedback structure. The result obtained shows that the minimum entropy solution of H ∞ optimal control problems can be obtained as an H 2 optimal solution. Therefore, it can be expected that the corresponding H ∞ optimal controller has an optimal observer-full state feedback structure 相似文献
2.
The authors correct the parameterization of the H ∞ controller of the full-information (FI) problem derived by J.C. Doyle et al. (1989). Then they parameterize the H m0 state feedback controller and explain how dynamical free parameters implied in it are related to constant feedback gains different from the central solution F ∞ 相似文献
3.
It is shown that D.S. Bernstein and W.M. Hadad's (ibid., vol.34, no.3, p.293, 1989) necessary condition for full-order mixed H 2 and H ∞ optimal control is also sufficient, and that J.C. Doyle et al.'s (Proc. Amer. Control Conf., p.2065, 1989) sufficient condition for full-order mixed H 2 and H ∞ optimal control is also necessary. They are duals of one another 相似文献
4.
Robust H ∞ control design for linear systems with uncertainty in both the state and input matrices is treated. A state feedback control design which stabilizes the plant and guarantees an H ∞-norm bound constraint on disturbance attenuation for all admissible uncertainties is presented. The robust H ∞ control problem is solved via the notion of quadratic stabilization with an H ∞ -norm bound. Necessary and sufficient conditions for quadratic stabilization with an H ∞-norm bound are derived. The results can be regarded as extensions of existing results on H ∞ control and robust stabilization of uncertain linear systems 相似文献
5.
A linear algorithm and a nonlinear algorithm for the problem of system identification in H ∞ posed by Helmicki et al. (1990) for discrete-time systems are presented. The authors derive some error bounds for the linear algorithm which indicate that it is not robustly convergent. However, the worst-case identification error is shown to grow as log(n ), where n is the model order. A robustly convergent nonlinear algorithm is derived, and bounds on the worst-case identification error (in the H ∞ norm) are obtained 相似文献
6.
Previously obtained results on L 2-gain analysis of smooth nonlinear systems are unified and extended using an approach based on Hamilton-Jacobi equations and inequalities, and their relation to invariant manifolds of an associated Hamiltonian vector field. On the basis of these results a nonlinear analog is obtained of the simplest part of a state-space approach to linear H ∞ control, namely the state feedback H ∞ optimal control problem. Furthermore, the relation with H ∞ control of the linearized system is dealt with 相似文献
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The suboptimality of some parameter for H ∞ -optimization by dynamic state-feedback is characterized in terms of the solvability of Riccati inequalities. This is done without restricting the finite zero structure of the plant. If there are no system zeros on the imaginary axis, the H ∞-problem can be treated in a complete and satisfactory way. Explicit characterizations optimum to be achieved are provided, and a closed formula for the optimal value is derived in terms of the H ∞-norm of some fixed transfer matrix. If the optimum is not attained, any sequence of controllers of bounded size which is constructed to approach the infimal norm must necessarily be high-gain. A globally and quadratically convergent algorithm to compute the optimal value is proposed. This algorithm is generalized to the H ∞-optimization problem by measurement feedback 相似文献
9.
The author clarifies some of the results of J.C. Doyle et al. (ibid., vol.34, no.8, p.831-47, Aug. 1989) and gives some new interpretations. In particular, the author parameterizes all suboptimal H ∞ controllers for the full information (FI) and state feedback control problems and indicates when this FI H ∞ control problem can or cannot be given a differential game saddle point interpretation 相似文献
10.
The authors apply H ∞-designed controllers to a generic VSTOL (vertical and short takeoff and landing) aircraft model GVAM. The design study motivates the use of H ∞ techniques, and addresses some of the implementation issues which arise for multivariable and H ∞-designed controllers. An approach for gain scheduling H ∞ controllers on the basis of the normalized comprime factor robust stabilization problem formulation used for the H ∞ design is developed. It utilizes the observer structure unique to this particular robustness optimization. A weighting selection procedure, has been developed for the associated loop-shaping technique used to specify performance. Multivariable controllers pose additional problems in the event of actuator saturations, and a desaturation scheme which accounts for this is applied to the GVAM. A comprehensive control law was developed and evaluated using the Royal Aerospace Establishment piloted simulation facility 相似文献
11.
A general state-space representation is used to allow a complete formulation of the H ∞ optimization problem without any invertibility condition on the system matrix, unlike existing solutions. A straightforward approach is used to solve the one-block H ∞ optimization problem. The parameterization of all solutions to the discrete-time H ∞ suboptimal one-block problem is first given in transfer function form in terms of a set of functions in H ∞ that satisfy a norm bound. The parameterization of all solutions is also given as a linear fractional representation 相似文献
12.
The H 2-optimal control of continuous-time linear time-invariant systems by sampled-data controllers is discussed. Two different solutions, state space and operator theoretic, are given. In both cases, the H 2 sampled-data problem is shown to be equivalent to a certain discrete-time H 2 problem. Other topics discussed include input-output stability of sampled-data systems, performance recovery in digital implementation of analog controllers, and sampled-data control of systems with the possibility of multiple-time delays 相似文献
13.
The problem of tightly bounding and shaping the frequency responses of two objective functions T i(s )( i =1,2) associated with a closed-loop system is considered. It is proposed that an effective way of doing this is to minimize (or bound) the function max {∥T 1(s )∥ ∞, ∥T 2(s)∥∞} subject to internal stability of the closed-loop system. The problem is formulated as an H ∞ control problem, and an iterative solution is given 相似文献
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The problems of H ∞ analysis and synthesis of discrete-time systems with block-diagonal real time-varying uncertainty are considered. It is shown that these problems can be converted into scaled H ∞ analysis and synthesis problems. The problems of quadratic stability analysis and quadratic stabilization of these types of systems are dealt with as a special case. The results on synthesis are established for general linear dynamic output feedback control 相似文献
16.
A state estimator is derived which minimizes the H ∞-norm of the estimation error power spectrum matrix. Two approaches are presented. The first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution. The second approach establishes a duality between the problem of H ∞-filtering and the problem of unconstrained input H ∞-optimal regulation. Using this duality, previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding Kalman filter. The two approaches usually lead to different results. They are compared by a simple example which also demonstrates a clear advantage of the H ∞-estimate over the conventional l 2-estimate 相似文献
17.
The worst-case effect of a disturbance system on the H 2 norm of the system is analyzed. An explicit expression is given for the worst-case H 2 norm when the disturbance system is allowed to vary over all nonlinear, time-varying and possibly noncausal systems with bounded L 2-induced operator norm. An upper bound for this measure, which is equal to the worst-case H 2 norm if the exogeneous input is scalar, is defined. Some further analysis of this upper bound is done, and a method to design controllers which minimize this upper bound over all robustly stabilizing controllers is given. The latter is done by relating this upper bound to a parameterized version of the auxiliary cost function studied in the literature 相似文献
18.
G. Stein (26th IEEE Conf. Decision Control, Los Angeles, CA, Dec. 1987) showed that H ∞ controller designs often give very unrealistic high-frequency behavior. The polynomial systems approach to H ∞ is used by the commenter to demonstrate that the high frequency gain of H ∞ controllers can be made to fall off at any desired rate provided improper noise and weighting models are chosen 相似文献
19.
An LQG (linear quadratic Gaussian) control-design problem involving a constraint on H ∞ disturbance attenuation is considered. The H ∞ performance constraint is embedded within the optimization process by replacing the covariance Lyapunov equation by a Riccati equation whose solution leads to an upper bound on L 2 performance. In contrast to the pair of separated Riccati equations of standard LQG theory, the H ∞-constrained gains are given by a coupled system of three modified Riccati equations. The coupling illustrates the breakdown of the separation principle for the H ∞ -constrained problem. Both full- and reduced-order design problems are considered with an H ∞ attenuation constraint involving both state and control variables. An algorithm is developed for the full-order design problem and illustrative numerical results are given 相似文献
20.
A solution is derived to the H ∞-optimization problem that arises in multivariable discrete-time regulation when the controller has full access to the state vector. The solution method is based on the close relations that exist between linear quadratic differential game theory and H ∞-optimization. The existing theory of discrete-time quadratic games is readily applied in order to derive the solution to a finite-time horizon version of the H ∞ -optimization problem. The solution of the infinite-time horizon H ∞-optimization problem is obtained by formally taking the limit of the number of stages to infinity 相似文献