Showing papers by "Petar V. Kokotovic published in 1995"
Book•
01 Jan 1995
TL;DR: In this paper, the focus is on adaptive nonlinear control results introduced with the new recursive design methodology -adaptive backstepping, and basic tools for nonadaptive BackStepping design with state and output feedbacks.
Abstract: From the Publisher:
Using a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping. Describes basic tools for nonadaptive backstepping design with state and output feedbacks.
6,923 citations
TL;DR: Simulations show that the use of the adaptive hysteresis inverse leads to major improvements of system performance.
Abstract: For a system with hysteresis, the authors present a parameterized hysteresis model and develop a hysteresis inverse. The authors then design adaptive controllers with an adaptive hysteresis inverse for plants with unknown hysteresis. A new adaptive controller structure is introduced which is capable of achieving a linear parameterization and a linear error model in the presence of a hysteresis nonlinearity. A robust adaptive law is used to update the controller parameters and hysteresis inverse parameters, which ensures the global boundedness of the closed-loop signals for a wide class of of hysteresis models. Simulations show that the use of the adaptive hysteresis inverse leads to major improvements of system performance. >
621 citations
TL;DR: A new adaptive nonlinear control design which achieves a complete controller-identifier separation and is more flexible than the Lyapunov-based design because the identifier can employ any standard update law gradient and least-squares, normalized and unnormalized.
Abstract: We present a new adaptive nonlinear control design which achieves a complete controller-identifier separation. This modularity is made possible by a strong input-to-state stability property of the new controller with respect to the parameter estimation error and its derivative as inputs. These inputs are independently guaranteed to be bounded by the identifier. The new design is more flexible than the Lyapunov-based design because the identifier can employ any standard update law gradient and least-squares, normalized and unnormalized. A key ingredient in the identifier design and convergence analysis is a nonlinear extension of the well-known linear swapping lemma. >
369 citations
TL;DR: An adaptive version of the authors' backlash inverse scheme is developed and applied to feedback control of a known linear plant with an unknown backlash at its input and results are used to illustrate achieved performance improvements.
Abstract: This paper addresses one of the nondifferentiable nonlinearities which appear very often in industrial control applications: backlash. The authors first present a right inverse of backlash and then give one of its possible implementations. Characteristics like backlash are seldom known, so an adaptive version of the authors' backlash inverse is more suitable for applications. The authors develop an adaptive backlash inverse scheme and apply it to feedback control of a known linear plant with an unknown backlash at its input. The authors use simulation results to illustrate achieved performance improvements. >
160 citations
TL;DR: In this paper, the authors consider adaptive control via state feedback for a class of feedback linearizable discrete-time systems and employ a systematic procedure to design the controllers and the update laws for the so-called parametric-strict feedback form and the parametric pure feedback form.
Abstract: We consider adaptive control via state feedback for a class of feedback linearizable discrete-time systems. To parallel the development in adaptive nonlinear continuous-time control, we employ a systematic procedure to design the controllers and the update laws for the so-called parametric-strict-feedback form and the parametric-pure-feedback form. The geometric conditions that characterize this class of systems are given. Depending on the growth conditions of the nonlinearities, global boundedness and convergence are achieved with various update laws. We also develop adaptive indirect schemes with an observer-based identifier for the parametric-strict-feedback form. As a result, the drawback of overparametrization in direct schemes can be removed.
156 citations
TL;DR: Simulations show significant improvements of the system performance achieved by adaptive backlash inverse controllers for systems with unknown backlash at the plant output.
Abstract: Adaptive control schemes for systems with unknown backlash at the plant output are developed. In the case of known backlash, a backlash inverse controller guarantees exact output tracking. When the backlash characteristics are unknown, adaptive laws are designed to update the controller parameters and to guarantee bounded input-output stability. Simulations show significant improvements of the system performance achieved by such adaptive backlash inverse controllers. >
131 citations
TL;DR: In this paper, an adaptive deadzone inverse approach is developed for control of discrete-time systems with unknown deadzones at the input of linear dynamics, whose parameters are updated to cancel the effect of the deadzone, and a linear part is designed to achieve tracking of a reference signal by the system output.
Abstract: An adaptive deadzone inverse approach is developed for control of discrete-time systems with unknown deadzones at the input of linear dynamics. The proposed controller consists of an adaptive deadzone inverse, whose parameters are updated to cancel the effect of the deadzone, and a linear part, which is designed to achieve tracking of a reference signal by the system output. When the linear part of the system is known, its parameters are used to specify the parameters of the linear part of the controller. When the linear part of the plant is unknown, the linear control parameters are adaptively estimated. The control error caused by the adaptive deadzone inverse is expressed as a linearly parametrizable part plus a bounded disturbance. Adaptive laws which employ parameter projection are used to update the controller parameters. They are robust with respect to the bounded disturbance, and they result in parameter estimates needed to implement an adaptive deadzone inverse. We prove the closed-loop signal bo...
121 citations
21 Jun 1995
TL;DR: A new class of controllers for dynamic feedback linearizable systems which achieve asymptotic tracking of given state reference trajectories is presented, characterized by a formula whose design parameters directly describe the trade-off between control effort and tracking error.
Abstract: Presents a new class of controllers for dynamic feedback linearizable systems which achieve asymptotic tracking of given state reference trajectories These controllers are characterized by a formula whose design parameters directly describe the trade-off between control effort and tracking error For natural choices of these design parameters, this formula generates controllers which do not blindly cancel nonlinearities but rather counteract them only when they degrade the performance of the system Furthermore, these controllers are optimal with respect to sensible performance criteria and therefore possess desirable robustness properties
97 citations
13 Dec 1995
TL;DR: In this article, a new systematic method for nonlinear control design, backstepping, is applied to low-order compression system models, which achieves global asymptotic stability of both stall and surge in the presence of large uncertainties in the compressor model.
Abstract: A new systematic method for nonlinear control design-backstepping-is applied to low-order compression system models. Backstepping achieves global asymptotic stability of both stall and surge in the presence of large uncertainties in the compressor model. Throughout our presentation, we explore the control design implications of the nonlinear equilibrium properties of compressors.
92 citations
TL;DR: In this article, the adaptive control Lyapunov function (AClf) was proposed to stabilize nonlinear systems linear in unknown constant parameters, using Sontag's constructive proof of Artstein's theorem to design an adaptive controller.
75 citations
28 Sep 1995
TL;DR: Backstepping offers flexibilities not present in other nonlinear design procedures as mentioned in this paper, such as the possibility to avoid cancellation of useful nonlinearities, which are common in feedback linearization designs, require large control effort and cause nonrobustness.
Abstract: Backstepping offers flexibilities not present in other nonlinear design procedures One of them is the possibility to avoid cancellation of useful nonlinearities Such cancellations, which are common in feedback linearization designs, require large control effort and cause nonrobustness As an illustration of a design that avoids cancellations we develop controllers for the Moore-Greitzer model of a jet engine compressor system The resulting backstepping controllers use less control effort than feedback linearizing controllers
TL;DR: The proposed controller structure results in a linear parametrization which is crucial for developing adaptive update laws and it is proved the signal boundedness for the closed-loop system, and for a special case it is established asymptotic tracking.
TL;DR: Adaptive output-feedback schemes for a class of discrete-time systems whose continuous-time counterparts are the output- feedback canonical form are presented.
Abstract: We present adaptive output-feedback schemes for a class of discrete-time systems whose continuous-time counterparts are the output-feedback canonical form. We first develop a systematic design procedure for the deterministic case. Global boundedness and convergence are achieved with no restriction imposed on the nonlinearities. Then we proceed to develop an analogous design procedure for the adaptive case. Depending on the characteristics of the nonlinearities, global boundedness and convergence can be achieved with various update laws. A rank condition is required to ensure such properties for nonlinearities which are not globally Lipschitz. >
01 Jan 1995
TL;DR: In this article, the BCU method for direct stability analysis of electric power systems is used to model electric machines using integral manifolds and a parallel solution of linear equations by overlapping epsilon decompositions.
Abstract: Bifurcation-theoretic issues in the control of voltage collapse.- Reduced-order modeling of electric machines using integral manifolds.- The BCU method for direct stability analysis of electric power systems: theory and applications.- New algorithms for slow coherency aggregation of large power systems.- Computational complexity results in parametric robust stability analysis with power systems applications.- Damping and resonance in a high power switching circuit.- Dynamic analysis of voltage collapse in power systems.- Exact convergence of a parallel textured algorithm for constrained economic dispatch control problems.- Variable structure regulation of power plant drum level.- Analysis of mechanisms of voltage instability in electric power systems.- Structural stability in power systems.- Power system load modeling.- Parallel solutions of linear equations by overlapping epsilon decompositions.- Insects, fish and computer-based super-agents.- Application of real-time phasor measurements in power system control.- On the dynamics of differential-algebraic systems such as the balanced large electric power system.- Robust stabilization of controls in power systems.
13 Dec 1995
TL;DR: In this article, a new approach to design controllers for global asymptotic stabilization of cascade and feedforward nonlinear systems is presented, where conditions for global stability and construct a continuously differentiable Lyapunov function for a class of uncontrolled cascade systems.
Abstract: We present a new approach to design controllers for global asymptotic stabilization of cascade and feedforward nonlinear systems. First we give conditions for global stability and construct a continuously differentiable Lyapunov function for a class of uncontrolled cascade systems. We use this Lyapunov function to design globally asymptotically stabilizing feedback laws for controlled cascade systems and, by applying the method recursively, for feedforward systems.
13 Dec 1995
TL;DR: For a class of systems with uncertain nonlinearities, the authors design robust integral controllers which achieve the tracking of constant reference signals which are of lower order than adaptive controllers would be were parameterizations of the uncertainties available.
Abstract: For a class of systems with uncertain nonlinearities, the authors design robust integral controllers which achieve the tracking of constant reference signals. No parameterizations of the uncertain functions are needed, and robustness with respect to exogenous disturbances is guaranteed. High gain is needed only for disturbance rejection; in the absence of disturbances, convergence of the tracking error to zero is achieved without high gain. These integral controllers are generally of lower order than adaptive controllers would be were parameterizations of the uncertainties available.
21 Jun 1995
TL;DR: In this article, the problem of feedback stabilization of translational oscillations by a rotational actuator (TORA) system is considered and several controller designs based on the cascade and passivity paradigms are presented.
Abstract: Considers the problem of feedback stabilization of translational oscillations by a rotational actuator (TORA system). The authors present several controller designs based on the cascade and passivity paradigms.
TL;DR: In this article, the authors construct dynamic partial state feedback controllers that achieve the global asymptotic tracking of given reference trajectories while maintaining internal boundedness for nonlinear systems in extended strict feedback form.
TL;DR: This article developed tools for backstepping with Lyapunov functions and control laws which are locally Lipschitz but not differentiable, using Clarke's generalized gradient and its associated calculus.
21 Jun 1995
TL;DR: In this article, the authors employ energy-based arguments to establish a robustness and a convergence result for a gradient-descent adaptive law in the presence of both noisy measurements and uncertainty in the initial guess.
Abstract: The authors employ energy-based arguments to establish a robustness and a convergence result for a gradient-descent adaptive law in the presence of both noisy measurements and uncertainty in the initial guess.
21 Jun 1995
TL;DR: In this paper, the adaptive control via state feedback for linear systems with input constraints is addressed, and an adaptive tracking design for stable systems in the observable canonical form and the parametric-strict feedback form with a chain of integrators is presented.
Abstract: The problems of adaptive control via state feedback for linear systems with input constraints are addressed. We first study an adaptive tracking design for stable systems in the observable canonical form. Then we consider plants both in the observable canonical form and the parametric-strict-feedback form with a chain of integrators. Our main design tool is backstepping. For both cases, our adaptive controllers ensure global boundedness without restricting the magnitude of the reference signal. However, to achieve perfect tracking certain magnitude constraints on the reference signal are required.
13 Dec 1995
TL;DR: In this paper, a linear backstepping controller combined with two types of identifiers, the passive identifier and the swapping identifier, is proposed to guarantee stability and performance without adaptation, which is an advantage of the estimation-based designs over the traditional ones.
Abstract: The authors previously introduced a class of adaptive nonlinear controllers which abandon the certainty equivalence principle and employ the backstepping approach with tuning functions. In this paper the authors introduce estimation-based designs which use a linear backstepping controller combined with two types of identifiers-the passive identifier and the swapping identifier. The linear backstepping controller can guarantee stability and performance without adaptation. This is an advantage of the estimation-based designs in this paper over the traditional ones.
01 Jan 1995
TL;DR: In this paper, the authors present an approach to adaptive nonlinear control based on a complete controller-identifier separation, which guarantees certain input/state stability properties with respect to the parameter error.
Abstract: We present a new approach to adaptive nonlinear control based on a complete controller-identifier separation which has long been a goal in adaptive system design. Our controllers guarantee certain input/state stability properties with respect to the parameter error % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiqaca0fcuaH4oqCgaacaaaa!3CEC! \[ \tilde \theta \] and its derivative % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiqaca0fcuaH4oqCgaacgaGaaaaa!3CF4! \[ \dot \tilde \theta \] as inputs. The parameter identifiers, in turn, guarantee % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiGacWefca0fcuaH4oqCgaacaiabgIGioprr1ngBPrwt % HrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae8NeHWKaeyOhIukaaa!4AD4! \[ \tilde \theta \in \mathcal{L}\infty \] , and either % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiGacWefca0fcuaH4oqCgaacgaGaaiabgIGioprr1ngB % PrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae8NeHWKaeyOhIu % kaaa!4ADC! \[ \dot \tilde \theta \in \mathcal{L}\infty \] or % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXgatC % vAUfeBSjuyZL2yd9gzLbvyNv2CaeHbd9wDYLwzYbItLDharyavP1wz % ZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbb % L8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpe % pae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaam % aaeaqbaaGcbiGacWefca0fcuaH4oqCgaacgaGaaiabgIGioprr1ngB % PrwtHrhAXaqehuuDJXwAKbstHrhAG8KBLbacgaGae8NeHW0aaSbaaS % qaaiabikdaYaqabaaaaa!4A89! \[ \dot \tilde \theta \in \mathcal{L}_2 \] or both. This estimation-based approach encompases two families of schemes: swapping-based and observer-based. Swapping-based schemes allow the use of a wide variety of update laws — gradient and least-squares, normalized and unnormalized. Observer-based schemes use parameter identifiers of lower dynamic order. All these schemes achieve systematic improvement of transient performance.
TL;DR: Two control Lyapunov function frameworks are presented for stabilization of nonlinear systems with unknown constant parameters and the problem is reduced to input-to-state stabilization with respect to parametric disturbance inputs.