This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in ...a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design.
Impulsive and hybrid dynamical systems Haddad, Wassim M; Chellaboina, VijaySekhar; Nersesov, Sergey G
2014., 20140908, 2006, 2006-01-01, Letnik:
15
eBook
This book develops a general analysis and synthesis framework for impulsive and hybrid dynamical systems. Such a framework is imperative for modern complex engineering systems that involve ...interacting continuous-time and discrete-time dynamics with multiple modes of operation that place stringent demands on controller design and require implementation of increasing complexity--whether advanced high-performance tactical fighter aircraft and space vehicles, variable-cycle gas turbine engines, or air and ground transportation systems.
Impulsive and Hybrid Dynamical Systemsgoes beyond similar treatments by developing invariant set stability theorems, partial stability, Lagrange stability, boundedness, ultimate boundedness, dissipativity theory, vector dissipativity theory, energy-based hybrid control, optimal control, disturbance rejection control, and robust control for nonlinear impulsive and hybrid dynamical systems. A major contribution to mathematical system theory and control system theory, this book is written from a system-theoretic point of view with the highest standards of exposition and rigor. It is intended for graduate students, researchers, and practitioners of engineering and applied mathematics as well as computer scientists, physicists, and other scientists who seek a fundamental understanding of the rich dynamical behavior of impulsive and hybrid dynamical systems.
In this article, we address finite time stability in probability of discrete-time stochastic dynamical systems. Specifically, a stochastic comparison lemma is constructed along with a scalar system ...involving a generalized deadzone function to establish almost sure convergence and finite time stability in probability. This result is used to provide Lyapunov theorems for finite time stability in probability for Itô-type stationary nonlinear stochastic difference equations involving Lyapunov difference conditions on the minimum of the Lyapunov function itself along with a fractional power of the Lyapunov function. In addition, we establish sufficient conditions for almost sure lower semicontinuity of the stochastic settling-time capturing the average settling time behavior of the discrete-time nonlinear stochastic dynamical system. Furthermore, a stochastic finite-time optimal control framework is developed by exploiting connections between Lyapunov theory for finite time stability in probability and stochastic Bellman theory. In particular, we show that finite time stability in probability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that can clearly be seen to be the solution to the steady state form of the stochastic Bellman equation, and hence, guaranteeing both stochastic finite time stability and optimality.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Since finite-time convergence implies nonuniqueness of system solutions in reverse ...time, such systems possess non-Lipschitzian dynamics. Sufficient conditions for finite-time stability have been developed in the literature using continuous Lyapunov functions. In this technical note, we develop a framework for addressing the problem of optimal nonlinear analysis and feedback control for finite-time stability and finite-time stabilization. Finite-time stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that satisfies a differential inequality involving fractional powers. This Lyapunov function can clearly be seen to be the solution to a partial differential equation that corresponds to a steady-state form of the Hamilton-Jacobi-Bellman equation, and hence, guaranteeing both finite-time stability and optimality.
Finite-time stability involves dynamical systems whose trajectories converge to an equilibrium state in finite time. Sufficient conditions for finite-time stability have recently been developed in ...the literature for discrete-time dynamical systems. In this article, we build on these results to develop a framework for addressing the problem of optimal nonlinear analysis and feedback control for finite-time stability and finite-time stabilization for nonlinear discrete-time controlled dynamical systems. Finite-time stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function that satisfies a difference inequality involving fractional powers and a minimum operator. This Lyapunov function can clearly be seen to be the solution to a difference equation that corresponds to a steady-state form of the Bellman equation, and hence, guaranteeing both finite-time stability and optimality. Finally, a numerical example is presented to demonstrate the efficacy of the proposed finite-time discrete stabilization framework.
Thermodynamics Haddad, Wassim M; Haddad, Wassim M; Chellaboina, VijaySekhar ...
2005., 20090110, 2005, 2009, 2005-01-01, c2005, Letnik:
12
eBook
This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel ...formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth.
•A reinforcement learning (RL) algorithm is developed as a model-free method for the optimal closed-loop control of cancer chemotherapy drug dosing.•Simulation results are presented for three cases, ...namely, (1) an adult with cancer, (2) a pregnant women with cancer, and (3) an elderly patient who has cancer along with other critical illnesses.•Statistical analysis using 15 simulated patients are conducted.
The increasing threat of cancer to human life and the improvement in survival rate of this disease due to effective treatment has promoted research in various related fields. This research has shaped clinical trials and emphasized the necessity to properly schedule cancer chemotherapy to ensure effective and safe treatment. Most of the control methodologies proposed for cancer chemotherapy scheduling treatment are model-based. In this paper, a reinforcement learning (RL)-based, model-free method is proposed for the closed-loop control of cancer chemotherapy drug dosing. Specifically, the Q-learning algorithm is used to develop an optimal controller for cancer chemotherapy drug dosing. Numerical examples are presented using simulated patients to illustrate the performance of the proposed RL-based controller.
Partially stable systems involve dynamical systems whose motion lie in a subspace of the state space resulting in system stability with respect to part of the system's states. In this paper, we ...develop partial stability theorems for nonlinear continuous-time and discrete-time dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward loop and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems.
While adaptive control has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the necessity of high-gain learning rates to achieve ...fast adaptation can be a serious limitation of adaptive controllers. This is due to the fact that fast adaptation using high-gain learning rates can cause high-frequency oscillations in the control response resulting in system instability. In this note, we present a new adaptive control architecture for nonlinear uncertain dynamical systems to address the problem of achieving fast adaptation using high-gain learning rates. The proposed framework involves a new and novel controller architecture involving a modification term in the update law. Specifically, this modification term filters out the high-frequency content contained in the update law while preserving asymptotic stability of the system error dynamics. This key feature of our framework allows for robust, fast adaptation in the face of high-gain learning rates. Furthermore, we show that transient and steady-state system performance is guaranteed with the proposed architecture. Two illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.
Thermodynamics is a physical branch of science that governs the thermal behavior of dynamical systems from those as simple as refrigerators to those as complex as our expanding universe. The laws of ...thermodynamics involving conservation of energy and nonconservation of entropy are, without a doubt, two of the most useful and general laws in all sciences. The first law of thermodynamics, according to which energy cannot be created or destroyed, merely transformed from one form to another, and the second law of thermodynamics, according to which the usable energy in an adiabatically isolated dynamical system is always diminishing in spite of the fact that energy is conserved, have had an impact far beyond science and engineering. In this paper, we trace the history of thermodynamics from its classical to its postmodern forms, and present a tutorial and didactic exposition of thermodynamics as it pertains to some of the deepest secrets of the universe.
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