THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Time-delay systems: an overview of some recent advances and open problems

The technology of hydrodynamic modeling and marine craft motion control systems has progressed greatly in recent years. This timely survey includes the latest tools for analysis and design of advanced guidance, navigation and control systems and presents new material on underwater vehicles and surface vessels. Each section presents numerous case studies and applications, providing a practical understanding of how model-based motion control systems are designed.

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Handbook of Marine Craft Hydrodynamics and Motion Control: Fossen/Handbook of Marine Craft Hydrodynamics and Motion Control

The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification of classes of systems for which systematic decomposition approaches can result in effective and easily computable control laws. These two aspects are complementary, since the latter approaches are, typically, based upon the inductive verification of the validity of the former system properties under compositions (in the terminology used in [62], the “activation” of theoretical concepts leads to “constructive” control). This expository presentation addresses the first of these aspects, and in particular the precise formulation of questions of robustness with respect to disturbances, formulated in the paradigm of input to state stability. We provide an intuitive and informal presentation of the main concepts. More precise statements, especially about older results, are given in the cited papers, as well as in several previous surveys such as [103] and [105] (of which the present paper represents an update), but we provide a little more detail about relatively recent work. Regarding applications and extensions of the basic framework, we give some pointers to the literature, but we do not focus on feedback design and specific engineering problems; for the latter we refer the reader to textbooks such as [43], [60], [58], [96], [66], [27], [44].

Input to State Stability: Basic Concepts and Results

The latest technological progress in sensors, actuators and energy storage devices enables the developments of miniature VTOL systems. In this paper we present the results of two nonlinear control techniques applied to an autonomous micro helicopter called Quadrotor. A backstepping and a sliding-mode techniques. We performed various simulations in open and closed loop and implemented several experiments on the test-bench to validate the control laws. Finally, we discuss the results of each approach. These developments are part of the OS4 project in our lab.

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Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor

1 Introduction -- 1.1 Passivity, Optimality, and Stability -- 1.2 Feedback Passivation -- 1.3 Cascade Designs -- 1.4 Lyapunov Constructions -- 1.5 Recursive Designs -- 1.6 Book Style and Notation -- 2 Passivity Concepts as Design Tools -- 2.1 Dissipativity and Passivity -- 2.2 Interconnections of Passive Systems -- 2.3 Lyapunov Stability and Passivity -- 2.4 Feedback Passivity -- 2.5 Summary -- 2.6 Notes and References -- 3 Stability Margins and Optimality -- 3.1 Stability Margins for Linear Systems -- 3.2 Input Uncertainties -- 3.3 Optimality, Stability, and Passivity -- 3.4 Stability Margins of Optimal Systems -- 3.5 Inverse Optimal Design -- 3.6 Summary -- 3.7 Notes and References -- 4 Cascade Designs -- 4.1 Cascade Systems -- 4.2 Partial-State Feedback Designs -- 4.3 Feedback Passivation of Cascades -- 4.4 Designs for the TORA System -- 4.5 Output Peaking: an Obstacle to Global Stabilization -- 4.6 Summary -- 4.7 Notes and References -- 5 Construction of Lyapunov functions -- 5.1 Composite Lyapunov functions for cascade systems -- 5.2 Lyapunov Construction with a Cross-Term -- 5.3 Relaxed Constructions -- 5.4 Stabilization of Augmented Cascades -- 5.5 Lyapunov functions for adaptive control -- 5.6 Summary -- 5.7 Notes and references -- 6 Recursive designs -- 6.1 Backstepping -- 6.2 Forwarding -- 6.3 Interlaced Systems -- 6.4 Summary and Perspectives -- 6.5 Notes and References -- A Basic geometric concepts -- A.1 Relative Degree -- A.2 Normal Form -- A.3 The Zero Dynamics -- A.4 Right-Invertibility -- A.5 Geometric properties -- B Proofs of Theorems 3.18 and 4.35 -- B.1 Proof of Theorem 3.18 -- B.2 Proof of Theorem 4.35.

Constructive Nonlinear Control

Motivated by control Lyapunov functions and Razumikhin theorems on stability of time delay systems, we introduce the concept of control Lyapunov-Razumikhin functions (CLRF). The main reason for considering CLRFs is construction of robust stabilizing control laws for time delay systems. Most existing universal formulas that apply to CLFs, are not applicable to CLRFs. It turns out that the domination redesign control law applies, achieving global practical stability and, under an additional assumption, global asymptotic stability. This additional assumption is satisfied in the practically important case when the quadratic part of a CLRF is itself a CLRF for the Jacobian linearization of the system. The CLRF based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin. While, in general, construction of CLRFs is an open problem, we show that for several classes of time delay systems a CLRF can be constructed in a systematic way.

Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems

Presents a control design method for diesel engines equipped with a variable geometry turbocharger and an exhaust gas recirculation valve. Our control objective is to regulate the air-fuel ratio and the fraction of recirculated exhaust gas to their respective set points that depend on engine operating conditions. Interactions between the two actuators and nonlinear behavior of the system make the problem difficult to handle using classical control design methods. Instead, we employ a control Lyapunov function (CLF) based nonlinear control design method because it possesses a guaranteed robustness property equivalent to gain and phase margins. The CLF is constructed using input-output linearization of a reduced order diesel engine model. The controller has been tested in simulations on the full order model as well as experimentally in the dynamometer test cell.

Constructive Lyapunov control design for turbocharged diesel engines

We present a global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results. Our main tool is the construction of a Lyapunov function for a class of (globally stable) uncontrolled cascade systems. This construction serves as a basis for a recursive controller design for cascade and feedforward systems. We give conditions for continuous differentiability of the Lyapunov function and the resulting control law and propose methods for their exact and approximate computation.

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Mrdjan J. Jankovic

Papers

Constructive Nonlinear Control

Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems

Constructive Lyapunov control design for turbocharged diesel engines

Constructive Lyapunov stabilization of nonlinear cascade systems

Robust control barrier functions for constrained stabilization of nonlinear systems