2,624 research outputs found
3 sampled-data control of nonlinear systems
This chapter provides some of the main ideas resulting from recent developments in sampled-data control of nonlinear systems. We have tried to bring the basic parts of the new developments within the comfortable grasp of graduate students. Instead of presenting the more general results that are available in the literature, we opted to present their less general versions that are easier to understand and whose proofs are easier to follow. We note that some of the proofs we present have not appeared in the literature in this simplified form. Hence, we believe that this chapter will serve as an important reference for students and researchers that are willing to learn about this area of research
Optimal sampled-data control, and generalizations on time scales
In this paper, we derive a version of the Pontryagin maximum principle for
general finite-dimensional nonlinear optimal sampled-data control problems. Our
framework is actually much more general, and we treat optimal control problems
for which the state variable evolves on a given time scale (arbitrary non-empty
closed subset of R), and the control variable evolves on a smaller time scale.
Sampled-data systems are then a particular case. Our proof is based on the
construction of appropriate needle-like variations and on the Ekeland
variational principle.Comment: arXiv admin note: text overlap with arXiv:1302.351
Randomly Sampled-Data Control Systems
The purpose is to solve the Linear Quadratic Regulator (LQR) problem with random time sampling. Such a sampling scheme may arise from imperfect instrumentation as in the case of sampling jitter. It can also model the stochastic information exchange among decentralized controllers to name just a few. A practical suboptimal controller is proposed with the nice property of mean square stability. The proposed controller is suboptimal in the sense that the control structure is limited to be linear. Because of i. i. d. assumption, this does not seem unreasonable. Once the control structure is fixed, the stochastic discrete optimal control problem is transformed into an equivalent deterministic optimal control problem with dynamics described by the matrix difference equation. The N-horizon control problem is solved using the Lagrange's multiplier method. The infinite horizon control problem is formulated as a classical minimization problem. Assuming existence of solution to the minimization problem, the total system is shown to be mean square stable under certain observability conditions. Computer simulations are performed to illustrate these conditions
Special purpose computer provides programmable digital filter for sampled-data control systems
Generalized digital filter is a special purpose computer. The term digital filter is an algorithm which accepts an input sequence of numbers and transforms it into an output number sequence. The organization of the computer, the logical design and synthesis, and experimentaion with the computer in two sampled data control systems is discussed
Distributed sampled-data control of nonholonomic multi-robot systems with proximity networks
This paper considers the distributed sampled-data control problem of a group
of mobile robots connected via distance-induced proximity networks. A dwell
time is assumed in order to avoid chattering in the neighbor relations that may
be caused by abrupt changes of positions when updating information from
neighbors. Distributed sampled-data control laws are designed based on nearest
neighbour rules, which in conjunction with continuous-time dynamics results in
hybrid closed-loop systems. For uniformly and independently initial states, a
sufficient condition is provided to guarantee synchronization for the system
without leaders. In order to steer all robots to move with the desired
orientation and speed, we then introduce a number of leaders into the system,
and quantitatively establish the proportion of leaders needed to track either
constant or time-varying signals. All these conditions depend only on the
neighborhood radius, the maximum initial moving speed and the dwell time,
without assuming a prior properties of the neighbor graphs as are used in most
of the existing literature.Comment: 15 pages, 3 figure
Research study on stabilization and control modern sampled-data control theory
The methods of continuous and discrete describing function analysis were applied to predicting the existence of self-sustained oscillations in the single-axis model of the large space telescope system with nonlinear control moment gyroscope friction characteristics. It is shown that the stability equations may be solved by a numerical-iterative technique using the describing function analysis, instead of the usual graphical methods. The numerical method is found to be effective in leading to a convergent solution rapidly, with an appropriate guess of the initial condition
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