Control Systems¶

Plant models and closed-loop neural network control system classes.

Plant Models¶

Continuous-time linear system: x’ = Ax + Bu, y = Cx + Du.

plant = LinearODE(A, B, C, D)
plant = LinearODE(A, B, C, D, controlPeriod, numReachSteps)

Key Properties: A, B, C, D, dim, nI, nO, controlPeriod, numReachSteps

Discrete-time linear system: x[k+1] = Ax[k] + Bu[k].

plant = DLinearODE(A, B, C, D)

Continuous-time nonlinear system via CORA. x’ = f(x, u, t), y = Cx.

plant = NonLinearODE(nVars, nInputs, @dynamics_func, reachStep, controlPeriod, outputMat)

CORA Options: taylorTerms, zonotopeOrder, maxError, tensorOrder, alg, reductionTechnique

Discrete-time nonlinear system.

plant = DNonLinearODE(nVars, nInputs, @dynamics_func, outputMat)

Hybrid automaton (switched systems) via CORA.

plant = HybridA(nModes, nVars, nInputs, dynamics, ...)

Class	Plant Type	Time	Constructor
`LinearNNCS`	LinearODE	Continuous	`LinearNNCS(controller, plant)`
`NonlinearNNCS`	NonLinearODE	Continuous	`NonlinearNNCS(controller, plant)`
`DLinearNNCS`	DLinearODE	Discrete	`DLinearNNCS(controller, plant)`
`DNonlinearNNCS`	DNonLinearODE	Discrete	`DNonlinearNNCS(controller, plant)`
`HybridANNCS`	HybridA	Hybrid	`HybridANNCS(controller, plant)`

Common Properties: feedbackMap, ref_I (reference input set), init_set

Common Methods:

[reachSets, simTraces, controlTraces] = nncs.reach(reachPRM)

where reachPRM contains: init_set, ref_input, numSteps, reachMethod, numCores