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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.
Consider a physical system modeled in state-space representation. 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 ...
A control flow node is used to control the subtasks of which it is composed. A control flow node may be either a selector (fallback) node or a sequence node. They run each of their subtasks in turn. When a subtask is completed and returns its status (success or failure), the control flow node decides whether to execute the next subtask or not.
In control theory, Ackermann's formula is a control system design method for solving the pole allocation problem for invariant-time systems by Jürgen Ackermann. [1] One of the primary problems in control system design is the creation of controllers that will change the dynamics of a system by changing the eigenvalues of the matrix representing the dynamics of the closed-loop system. [2]
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .
In control theory, a distributed-parameter system (as opposed to a lumped-parameter system) is a system whose state space is infinite-dimensional. Such systems are therefore also known as infinite-dimensional systems. Typical examples are systems described by partial differential equations or by delay differential equations.
For the simplest example of a continuous, LTI system, the row dimension of the state space expression ˙ = + determines the interval; each row contributes a vector in the state space of the system. If there are not enough such vectors to span the state space of x {\displaystyle \mathbf {x} } , then the system cannot achieve controllability.
Lagrangian formulation is used to determine the system equations of motion. Lyapunov stability theory is used to develop the cooperative control by using a reference trajectory and reference actuator torques. Polynomial curves represent potential reference trajectories.