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The costate equation is related to the state equation used in optimal control. [1] [2] It is also referred to as auxiliary, adjoint, influence, or multiplier equation.It is stated as a vector of first order differential equations
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
The asymptotic availability, i.e. availability over a long period, of the system is equal to the probability that the model is in state 1 or state 2. This is calculated by making a set of linear equations of the state transition and solving the linear system. The matrix is constructed with a row for each state.
Complete state controllability (or simply controllability if no other context is given) describes the ability of an external input (the vector of control variables) to move the internal state of a system from any initial state to any final state in a finite time interval. [1]: 737
In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, [citation needed] a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs ...
In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.
State based control can be thought of as an extension of the unit operation concept in the process industry. [7] Processes are designed with unit operations. With state-based control the control design is divided into units and those units further divided into states, with the proper operating discipline for each state designed in.
A system is said to be observable if, for every possible evolution of state and control vectors, the current state can be estimated using only the information from outputs (physically, this generally corresponds to information obtained by sensors). In other words, one can determine the behavior of the entire system from the system's outputs.