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Together, the state and costate equations describe the Hamiltonian dynamical system (again analogous to but distinct from the Hamiltonian system in physics), the solution of which involves a two-point boundary value problem, given that there are boundary conditions involving two different points in time, the initial time (the differential ...
For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems. Mathematically, this means that for a causal linear system to be stable all of the poles of its transfer function must have negative-real values, i.e. the real part of each pole must be less than zero.
In control engineering, a discrete-event dynamic system (DEDS) is a discrete-state, event-driven system of which the state evolution depends entirely on the occurrence of asynchronous discrete events over time.
A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
Dynamical systems theory and chaos theory deal with the long-term qualitative behavior of dynamical systems.Here, the focus is not on finding precise solutions to the equations defining the dynamical system (which is often hopeless), but rather to answer questions like "Will the system settle down to a steady state in the long term, and if so, what are the possible steady states?", or "Does ...
which is known as the discrete-time dynamic Riccati equation of this problem. The steady-state characterization of P, relevant for the infinite-horizon problem in which T goes to infinity, can be found by iterating the dynamic equation repeatedly until it converges; then P is characterized by removing the time subscripts from the dynamic equation.
Optimal control problem benchmark (Luus) with an integral objective, inequality, and differential constraint. Optimal control theory is a branch of control theory that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. [1]
Digital control theory is the technique to design strategies in discrete time, (and/or) quantized amplitude (and/or) in (binary) coded form to be implemented in computer systems (microcontrollers, microprocessors) that will control the analog (continuous in time and amplitude) dynamics of analog systems.