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008 Computing the H∞ norm for nonlinear systems
Abstracts Abstracts in this section are from papers presented at: 12th IFAC TRIENNIAL WORLD CONGRESS ON AUTOMATIC CONTROL (VOLUME 1) Sydney, Australia, 18-23 July 1993 Full papers appear in the Proceedings volume to which the page numbers relate, published by IFAC and available from Elsevier Science (ISBN: 0 08 042212 8)
001
the feedback loops opens because of a failure in the corresponding sensor and/or actuator.
Controller Design for Reliable Stabilization A.N. Giindes, pp 1-4
For linear, time-invariant, multi-input multi-output control systems, a reliable controller design method is developed; two controllers are designed to stabilize the closed-loop system, both when they act together and when either one fails completely. For stable plants, a method of decomposing a given stabilizing controller into the sum of two controllers is also developed, so that closed-loop stability is maintained when acting together or independently. 002
006
Referring to a locally robust multivariable regulation scheme based on the intemal model principle, the authors consider the problem of avoiding any transient on the error variables when the plant and/or the regulator are subject to sudden, large parameter changes, completely known in advance as to magnitude and time of occurrence. The task is achieved by means of a supervisor that receives information on the regulator state before changes and suitably sets the states of both the regulator and a special feedforward unit at the switching times. A complete set of solvability conditions is derived in geometric terms.
Reliable Stabilization Based on a Multi-Compensator Configuration N. Sebe, T. KitamorI, pp 5-8
This paper proposes a new multi-compensator configuration for the reliable stabilization problem. In the proposed configuration, each compensator observes the outputs of the other compensators. This configuration provides reliable stabilization against actuator failures. A sufficient condition for stability with this configuration is given in this paper. The transfer function of the closed-loop system is given explicitly.
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007
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Robust Integral Stabilization and Regulation of Uncertain Multivariable Systems O.D.I. Nwokah, C.H. Yau, R.A. Perez, pp 13-17
Computing the Ho~ Norm for Nonlinear Systems M.R. James, pp 31-34
This paper proposes a numerical technique for computing the H,o norm of input-output maps arising from nonlinear state-space systems. The numerical technique is based on the finite difference method and a version of the Bounded Real Lemma, which involves a partial differential inequality.
The recent concept of multivariable integral controllability (MIC) is generalized to uncertain multivariable systems. It is shown that MIC is strongly dependent on the all gain positive stability (AGPS) of the steady-state open-loop transfer matrix. Some sufficient conditions for AGPS are provided, from which a design scheme for inducing MIC on any given system can be determined. 005
Asymptotic Output Tracking for a Large Class of Uncertain SISO Nonlinear Systems: Stability Z. Retchkiman, pp 27-30
The problem of asymptotic output tracking in the presence of uncertainties is re-examined. A characterization of the class of uncertainties dealt with in this study is given. A study of the asymptotic output problem plus stability for the class of uncertainties allowed is also discussed. Then the paper makes a generalization to the case when there are singular points. Finally an example that illustrates the concepts proposed is presented.
Control Systems Possessing Reliability to Control Channel Outages J.V. Medanic, W.R. Perkins, pp 9-12
System reliability is an important design consideration whenever fault-tolerant operation must be maintained in the face of outrages. Graceful degradation of a reliable system allows times for diagnosis, fault isolation, control system restructuring, and continuous operation. A methodology for the design of reliable control systems using the Hoo norm to measure performance is presented.
004
Regulation Without Transients Under Large Parameter Jumps G. Marro, A. Piazzi, pp 23-26
009
Reliable Regulation of Multirate Sampled.Data Systems A. Locatelli, N. Schlavoni, pp 19-22
Transformation of Nonlinear Discrete-Time Systems into Observer Canonical Form R. Ingenbleek, pp 35-38
A linear differential operator enables a compact description of the observability matrix for discrete-time analytic systems. For systems in observer canonical form local observability is ensured. Recursive equations that determine the transformation into this canonical form are derived. For systems linear with respect to the states this transformation always exists, if the system is locally observable. As a technical application a continuous-time bilinear model of a translatory hydraulic drive is considered, which has a state affine discrete-time equivalent. A canonical form observer design for this example is outlined.
This paper is concerned with the design of multirate sampled-data control systems, i.e., systems where the updating and/or measurement mechanisms are non-standard. It addresses the general problem of synthesizing a decentralized regulator which guarantees stability as well as zero steady-state error despite the presence of unstable exogenous signals. Moreover, it is desired that these properties hold in a reliable way, i.e., not only when the closed-loop system is in nominal conditions, but also when one of
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001
the feedback loops opens because of a failure in the corresponding sensor and/or actuator.
Controller Design for Reliable Stabilization A.N. Giindes, pp 1-4
For linear, time-invariant, multi-input multi-output control systems, a reliable controller design method is developed; two controllers are designed to stabilize the closed-loop system, both when they act together and when either one fails completely. For stable plants, a method of decomposing a given stabilizing controller into the sum of two controllers is also developed, so that closed-loop stability is maintained when acting together or independently. 002
006
Referring to a locally robust multivariable regulation scheme based on the intemal model principle, the authors consider the problem of avoiding any transient on the error variables when the plant and/or the regulator are subject to sudden, large parameter changes, completely known in advance as to magnitude and time of occurrence. The task is achieved by means of a supervisor that receives information on the regulator state before changes and suitably sets the states of both the regulator and a special feedforward unit at the switching times. A complete set of solvability conditions is derived in geometric terms.
Reliable Stabilization Based on a Multi-Compensator Configuration N. Sebe, T. KitamorI, pp 5-8
This paper proposes a new multi-compensator configuration for the reliable stabilization problem. In the proposed configuration, each compensator observes the outputs of the other compensators. This configuration provides reliable stabilization against actuator failures. A sufficient condition for stability with this configuration is given in this paper. The transfer function of the closed-loop system is given explicitly.
003
007
008
Robust Integral Stabilization and Regulation of Uncertain Multivariable Systems O.D.I. Nwokah, C.H. Yau, R.A. Perez, pp 13-17
Computing the Ho~ Norm for Nonlinear Systems M.R. James, pp 31-34
This paper proposes a numerical technique for computing the H,o norm of input-output maps arising from nonlinear state-space systems. The numerical technique is based on the finite difference method and a version of the Bounded Real Lemma, which involves a partial differential inequality.
The recent concept of multivariable integral controllability (MIC) is generalized to uncertain multivariable systems. It is shown that MIC is strongly dependent on the all gain positive stability (AGPS) of the steady-state open-loop transfer matrix. Some sufficient conditions for AGPS are provided, from which a design scheme for inducing MIC on any given system can be determined. 005
Asymptotic Output Tracking for a Large Class of Uncertain SISO Nonlinear Systems: Stability Z. Retchkiman, pp 27-30
The problem of asymptotic output tracking in the presence of uncertainties is re-examined. A characterization of the class of uncertainties dealt with in this study is given. A study of the asymptotic output problem plus stability for the class of uncertainties allowed is also discussed. Then the paper makes a generalization to the case when there are singular points. Finally an example that illustrates the concepts proposed is presented.
Control Systems Possessing Reliability to Control Channel Outages J.V. Medanic, W.R. Perkins, pp 9-12
System reliability is an important design consideration whenever fault-tolerant operation must be maintained in the face of outrages. Graceful degradation of a reliable system allows times for diagnosis, fault isolation, control system restructuring, and continuous operation. A methodology for the design of reliable control systems using the Hoo norm to measure performance is presented.
004
Regulation Without Transients Under Large Parameter Jumps G. Marro, A. Piazzi, pp 23-26
009
Reliable Regulation of Multirate Sampled.Data Systems A. Locatelli, N. Schlavoni, pp 19-22
Transformation of Nonlinear Discrete-Time Systems into Observer Canonical Form R. Ingenbleek, pp 35-38
A linear differential operator enables a compact description of the observability matrix for discrete-time analytic systems. For systems in observer canonical form local observability is ensured. Recursive equations that determine the transformation into this canonical form are derived. For systems linear with respect to the states this transformation always exists, if the system is locally observable. As a technical application a continuous-time bilinear model of a translatory hydraulic drive is considered, which has a state affine discrete-time equivalent. A canonical form observer design for this example is outlined.
This paper is concerned with the design of multirate sampled-data control systems, i.e., systems where the updating and/or measurement mechanisms are non-standard. It addresses the general problem of synthesizing a decentralized regulator which guarantees stability as well as zero steady-state error despite the presence of unstable exogenous signals. Moreover, it is desired that these properties hold in a reliable way, i.e., not only when the closed-loop system is in nominal conditions, but also when one of
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