Basic Examples (8) 

A system that starts at -1:

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The state and input weights:

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The initial value of the gain:

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The total simulations is 30 with a batch consisting of 10 simulations:

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Compute the controller:

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The gain converges to ~0.1:

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The state is regulated to the origin:

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The input sequence that was used during the simulation:

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Scope (6) 

A system with one state and one input:

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Compute a controller:

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The gain values:

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The state is regulated to the origin:

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The input sequence that was used during the simulation:

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A multi-state system:

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Compute a controller:

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The gain values:

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The states are regulated to the origin:

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The input sequence that was used during the simulation:

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A multi-state, multi-input system:

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Compute a controller:

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The gain values:

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The states are regulated to the origin:

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The input sequence that was used during the simulation:

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A state-space model:

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Compute a controller:

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The gain values:

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The states are regulated to the origin:

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The input sequence that was used during the simulation:

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By default, a SystemsModelControllerData object is returned:

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It can be used to obtain various properties:

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The value of a specific property:

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A list of property values:

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The values of all properties as an Association:

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As a Dataset:

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Get a property directly:

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Applications (7) 

The model of the U.S Coast Guard cutter Tampa based on sea-trials data that gives the heading in response to rudder angle inputs:

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Discretize the model:

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The model is marginally stable:

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A Q-learning LQ regulator starting with an initial heading of 5°:

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The computed gain values:

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The heading is regulated back to the origin in about 20 seconds:

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The rudder input values:

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Properties and Relations (2) 

The gain computed by simulation converges to the optimal solution:

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The optimal solution computed with knowledge of the system's dynamics:

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The above solution is computed using the discrete algebraic Riccati equation:

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The gain computed by simulation converges to the optimal solution for a nonlinear system:

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The optimal solution computed using the linearized model:

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The above solution is computed using the discrete algebraic Riccati equation:

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Possible Issues (4) 

An unstable system may not converge to the optimal solution:

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Adjusting the initial gain causes it to converge to the optimal solution:

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The optimal solution:

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A system with a disturbance may not converge to the optimal solution:

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Adjusting the initial gain may cause it to come close to the optimal solution:

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The optimal solution:

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The initial gain must be stabilizing:

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Otherwise the state values will blow up:

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The state values with a stabilizing gain:

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The system must be a discrete-time system:

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