juhitavuse

Juhitavus, in control theory often translated as controllability, is the property of a dynamical system that allows its state to be steered from any initial state to any desired final state in finite time by an appropriate input, within given model and input constraints. A system is considered fully juhitav if this is possible for all state pairs; if not, some states or modes are uncontrollable.

For a continuous-time linear time-invariant system described by dx/dt = Ax + Bu, the system is juhitav if the Kalman rank condition holds: the controllability matrix [B AB A^2B ... A^{n-1}B] has full rank n, where n is the dimension of the state space. In discrete time, a similar criterion applies. When the condition is not met, there exists a nontrivial uncontrollable subspace, comprising states that cannot be reached from the origin through any allowable input sequence, and these uncontrollable modes cannot be shifted by control actions.

In nonlinear and time-varying systems, juhitavus is analyzed using different criteria. Local controllability can be studied via the Lie algebra generated by the system’s vector fields, with results such as Chow’s theorem providing conditions for local controllability under certain rank assumptions.

Applications of juhitavuse concepts span robotics, aerospace, process control, and any field involving system design and controller synthesis. Understanding controllability informs actuator placement, achievable performance, energy requirements, and the feasibility of steering a system to a desired state within constraints.