There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

1. Introduction. Control System Design Steps. Adaptive Control. A Brief History. 2. Models for Dynamic Systems. Introduction. State-Space Models. Input/Output Models. Plant Parametric Models. Problems. 3. Stability. Introduction. Preliminaries. Input/Output Stability. Lyapunov Stability. Positive Real Functions and Stability. Stability of LTI Feedback System. Problems. 4. On-Line Parameter Estimation. Introduction. Simple Examples. Adaptive Laws with Normalization. Adaptive Laws with Projection. Bilinear Parametric Model. Hybrid Adaptive Laws. Summary of Adaptive Laws. Parameter Convergence Proofs. Problems. 5. Parameter Identifiers and Adaptive Observers. Introduction. Parameter Identifiers. Adaptive Observers. Adaptive Observer with Auxiliary Input. Adaptive Observers for Nonminimal Plant Models. Parameter Convergence Proofs. Problems. 6. Model Reference Adaptive Control. Introduction. Simple Direct MRAC Schemes. MRC for SISO Plants. Direct MRAC with Unnormalized Adaptive Laws. Direct MRAC with Normalized Adaptive Laws. Indirect MRAC. Relaxation of Assumptions in MRAC. Stability Proofs in MRAC Schemes. Problems. 7. Adaptive Pole Placement Control. Introduction. Simple APPC Schemes. PPC: Known Plant Parameters. Indirect APPC Schemes. Hybrid APPC Schemes. Stabilizability Issues and Modified APPC. Stability Proofs. Problems. 8. Robust Adaptive Laws. Introduction. Plant Uncertainties and Robust Control. Instability Phenomena in Adaptive Systems. Modifications for Robustness: Simple Examples. Robust Adaptive Laws. Summary of Robust Adaptive Laws. Problems. 9. Robust Adaptive Control Schemes. Introduction. Robust Identifiers and Adaptive Observers. Robust MRAC. Performance Improvement of MRAC. Robust APPC Schemes. Adaptive Control of LTV Plants. Adaptive Control for Multivariable Plants. Stability Proofs of Robust MRAC Schemes. Stability Proofs of Robust APPC Schemes. Problems. Appendices. Swapping Lemmas. Optimization Techniques. Bibliography. Index. License Agreement and Limited Warranty.

Robust adaptive control

The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

Convergence of probability measures

https://users.encs.concordia.ca/~ymzhang/publications/ARC32-2-98Zhang_pp.229-252.pdf

Bibliographical review on reconfigurable fault-tolerant control systems

Autonomous vehicles (AVs) represent a potentially disruptive yet beneficial change to our transportation system. This new technology has the potential to impact vehicle safety, congestion, and travel behavior. All told, major social AV impacts in the form of crash savings, travel time reduction, fuel efficiency and parking benefits are estimated to approach $2000 to per year per AV, and may eventually approach nearly $4000 when comprehensive crash costs are accounted for. Yet barriers to implementation and mass-market penetration remain. Initial costs will likely be unaffordable. Licensing and testing standards in the U.S. are being developed at the state level, rather than nationally, which may lead to inconsistencies across states. Liability details remain undefined, security concerns linger, and without new privacy standards, a default lack of privacy for personal travel may become the norm. The impacts and interactions with other components of the transportation system, as well as implementation details, remain uncertain. To address these concerns, the federal government should expand research in these areas and create a nationally recognized licensing framework for AVs, determining appropriate standards for liability, security, and data privacy.

https://www.aamva.org/WorkArea/DownloadAsset.aspx?id=6738

Preparing a nation for autonomous vehicles: opportunities, barriers and policy recommendations

A robust adaptive nonlinear control design

A multi-input/multi-output adaptive sliding controller is designed and analyzed for the longitudinal dynamics of a generic hypersonic air vehicle. This vehicle model is nonlinear, multivariable, and unstable and includes uncertain parameters. Simulation studies are conducted for trimmed cruise conditions of 110,000 ft and Mach 15 where the responses of the vehicle to a step change in altitude and airspeed are evaluated. The commands are 100-ft/s step velocity and 2000-ft step altitude. The controller is evaluated for robustness with respect to parameter uncertainties using simulations. Simulation studies demonstrate that the proposed controller is robust with respect to parametric uncertainty and meets the performance requirements with relatively low-amplitude control inputs.

Adaptive Sliding Mode Control Design for a Hypersonic Flight Vehicle

Several continuous-time and discrete-time recurrent neural network models have been developed and applied to various engineering problems. One of the difficulties encountered in the application of recurrent networks is the derivation of efficient learning algorithms that also guarantee the stability of the overall system. This paper studies the approximation and learning properties of one class of recurrent networks, known as high-order neural networks; and applies these architectures to the identification of dynamical systems. In recurrent high-order neural networks, the dynamic components are distributed throughout the network in the form of dynamic neurons. It is shown that if enough high-order connections are allowed then this network is capable of approximating arbitrary dynamical systems. Identification schemes based on high-order network architectures are designed and analyzed. >

High-order neural network structures for identification of dynamical systems

Preface Acknowledgements List of acronyms 1. Introduction 2. Parametric models 3. Parameter identification: continuous time 4. Parameter identification: discrete time 5. Continuous-time model reference adaptive control 6. Continuous-time adaptive pole placement control 7. Adaptive control for discrete-time systems 8. Adaptive control of nonlinear systems Appendix Bibliography Index.

Petros Ioannou

Papers

Robust adaptive control

A robust adaptive nonlinear control design

Adaptive Sliding Mode Control Design for a Hypersonic Flight Vehicle

High-order neural network structures for identification of dynamical systems

Adaptive control tutorial