Ebook: Sliding Modes in Control and Optimization

The book is devoted to systems with discontinuous control. The study of discontinuous dynamic systems is a multifacet problem which embraces mathematical, control theoretic and application aspects. Times and again, this problem has been approached by mathematicians, physicists and engineers, each profession treating it from its own positions. Interestingly, the results obtained by specialists in different disciplines have almost always had a significant effect upon the development of the control theory. It suffices to mention works on the theory of oscillations of discontinuous nonlinear systems, mathematical studies in ordinary differential equations with discontinuous righthand parts or variational problems in nonclassic statements. The unremitting interest to discontinuous control systems enhanced by their effective application to solution of problems most diverse in their physical nature and functional purpose is, in the author's opinion, a cogent argument in favour of the importance of this area of studies. It seems a useful effort to consider, from a control theoretic viewpoint, the mathematical and application aspects of the theory of discontinuous dynamic systems and determine their place within the scope of the present-day control theory. The first attempt was made by the author in 1975-1976 in his course on "The Theory of Discontinuous Dynamic Systems" and "The Theory of Variable Structure Systems" read to post-graduates at the University of Illinois, USA, and then presented in 1978-1979 at the seminars held in the Laboratory of Systems with Discontinous Control at the Institute of Control Sciences in Moscow.

---

The purpose of this book is to describe a new approach for the design of high-efficiency control of multi-dimensional systems operating under uncertainty conditions. It covers mathematical, control and technological aspects of discontinuous control systems. The generation of sliding modes is the basic design idea resulting in decomposition of system motion and invariancy to uncertainties in plant behaviour. Implementation of discontinuous control is natural for widely used electronic power converters with key operation.

---

The purpose of this book is to describe a new approach for the design of high-efficiency control of multi-dimensional systems operating under uncertainty conditions. It covers mathematical, control and technological aspects of discontinuous control systems. The generation of sliding modes is the basic design idea resulting in decomposition of system motion and invariancy to uncertainties in plant behaviour. Implementation of discontinuous control is natural for widely used electronic power converters with key operation.
Content:
Front Matter....Pages I-XVI
Scope of the Theory of Sliding Modes....Pages 1-11
Mathematical Description of Motions on Discontinuity Boundaries....Pages 12-28
The Uniqueness Problems....Pages 29-43
Stability of Sliding Modes....Pages 44-65
Singularly Perturbed Discontinuous Systems....Pages 66-73
Front Matter....Pages 75-75
Decoupling in Systems with Discontinuous Controls....Pages 76-90
Eigenvalue Allocation....Pages 91-110
Systems with Scalar Control....Pages 111-130
Dynamic Optimization....Pages 131-144
Control of Linear Plants in the Presence of Disturbances....Pages 145-154
Systems with High Gains and Discontinuous Controls....Pages 155-168
Control of Distributed-Parameter Plants....Pages 169-188
Control Under Uncertainty Conditions....Pages 189-205
State Observation and Filtering....Pages 206-222
Sliding Modes in Problems of Mathematical Programming....Pages 223-236
Front Matter....Pages 237-238
Manipulator Control System....Pages 239-249
Sliding Modes in Control of Electric Motors....Pages 250-264
Examples....Pages 265-277
Back Matter....Pages 278-286

---

The purpose of this book is to describe a new approach for the design of high-efficiency control of multi-dimensional systems operating under uncertainty conditions. It covers mathematical, control and technological aspects of discontinuous control systems. The generation of sliding modes is the basic design idea resulting in decomposition of system motion and invariancy to uncertainties in plant behaviour. Implementation of discontinuous control is natural for widely used electronic power converters with key operation.
Content:
Front Matter....Pages I-XVI
Scope of the Theory of Sliding Modes....Pages 1-11
Mathematical Description of Motions on Discontinuity Boundaries....Pages 12-28
The Uniqueness Problems....Pages 29-43
Stability of Sliding Modes....Pages 44-65
Singularly Perturbed Discontinuous Systems....Pages 66-73
Front Matter....Pages 75-75
Decoupling in Systems with Discontinuous Controls....Pages 76-90
Eigenvalue Allocation....Pages 91-110
Systems with Scalar Control....Pages 111-130
Dynamic Optimization....Pages 131-144
Control of Linear Plants in the Presence of Disturbances....Pages 145-154
Systems with High Gains and Discontinuous Controls....Pages 155-168
Control of Distributed-Parameter Plants....Pages 169-188
Control Under Uncertainty Conditions....Pages 189-205
State Observation and Filtering....Pages 206-222
Sliding Modes in Problems of Mathematical Programming....Pages 223-236
Front Matter....Pages 237-238
Manipulator Control System....Pages 239-249
Sliding Modes in Control of Electric Motors....Pages 250-264
Examples....Pages 265-277
Back Matter....Pages 278-286
....