Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems
Control Lyapunov functions for homogeneous “Jurdjevic-Quinn” systems
This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a control Lyapunov function can be obtained via a deformation of this “weak” Lyapunov function. Some examples are presented, and the linear quadratic situation is treated as an illustration.
Control norms for large control times
Control Norms for Large Control Times
A control system of the second order in time with control is considered. If the system is controllable in a strong sense and uT is the control steering the system to the rest at time T, then the L2–norm of uT decreases as while the –norm of uT is approximately constant. The proof is based on the moment approach and properties of the relevant exponential family. Results are applied to the wave equation with boundary or distributed controls.
Control of a clamped-free beam by a piezoelectric actuator
We consider a controllability problem for a beam, clamped at one boundary and free at the other boundary, with an attached piezoelectric actuator. By Hilbert Uniqueness Method (HUM) and new results on diophantine approximations, we prove that the space of exactly initial controllable data depends on the location of the actuator. We also illustrate these results with numerical simulations.
Control of a class of chaotic systems by a stochastic delay method
A delay stochastic method is introduced to control a certain class of chaotic systems. With the Lyapunov method, a suitable kind of controllers with multiplicative noise is designed to stabilize the chaotic state to the equilibrium point. The method is simple and can be put into practice. Numerical simulations are provided to illustrate the effectiveness of the proposed controllable conditions.
Control of a DC brush motor via dynamic output feedback. (Control por realimentación dinámica de salida de un motor DC.)
Control of a neoclassic economic model
Control of a team of mobile robots based on non-cooperative equilibria with partial coordination
In this work we present an application of the concept of non-cooperative game equilibria to the design of a collision free movement of a team of mobile robots in a dynamic environment. We propose the solution to the problem of feasible control synthesis, based on a partially centralized sensory system. The control strategy based on the concept of non-cooperative game equilibria is well known in the literature. It is highly efficient through phases where the solution is unique. However, even in simple...
Control of an induction motor using sliding mode linearization
Nonlinear control of the squirrel induction motor is designed using sliding mode theory. The developed approach leads to the design of a sliding mode controller in order to linearize the behaviour of an induction motor. The second problem described in the paper is decoupling between two physical outputs: the rotor speed and the rotor flux modulus. The sliding mode tools allow us to separate the control from these two outputs. To take account of parametric variations, a model-based approach is used...
Control of constrained nonlinear uncertain discrete-time systems via robust controllable sets: a modal interval analysis approach
A general framework for computing robust controllable sets of constrained nonlinear uncertain discrete-time systems as well as controlling such complex systems based on the computed robust controllable sets is introduced in this paper. The addressed one-step control approach turns out to be a robust model predictive control scheme with feasible unit control horizon and contractive constraint. The solver of 1-dimensional quantified set inversion in modal interval analysis is extended to 2-dimensional...
Control of distributed delay systems with uncertainties: a generalized Popov theory approach
The paper deals with the generalized Popov theory applied to uncertain systems with distributed time delay. Sufficient conditions for stabilizing this class of delayed systems as well as for -attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov–Krasovskii functional. The considered approach is new in the context of distributed linear time-delay systems and gives some interesting interpretations of memoryless control problems in terms of Popov triplets...
Control of initially unknown plants
Control of jump processes and applications
Control of linear systems with rational expectations. The case of incomplete information.
The problem of optimal control of linear economic systems with rational expectations and quadratic objective function is solved for the case of incomplete information. The case of complete information has been previously studied. In both problems the hypothesis of causality is not satisfied and, therefore, the standard techniques of control theory cannot be directly applied, though the method used is based on these techniques.
Control of networks of Euler-Bernoulli beams
Control of networks of Euler-Bernoulli beams
We consider the exact controllability problem by boundary action of hyperbolic systems of networks of Euler-Bernoulli beams. Using the multiplier method and Ingham's inequality, we give sufficient conditions insuring the exact controllability for all time. These conditions are related to the spectral behaviour of the associated operator and are sufficiently concrete in order to be able to check them on particular networks as illustrated on simple examples.
Control of nonholonomic systems via dynamic compensation
Control of oscillating systems with a single delay.
Control of quasi-differential equations