Solves the Riccati differential equation for the finite-horizon linear quadratic regulator.

NOTE: This function requires the IVP Solver Toolbox.

[t,P] = solve_riccati_ode(A,B,Q,R,[],PT,tspan)
[t,P] = solve_riccati_ode(A,B,Q,R,S,PT,tspan)

[t,P] = solve_riccati_ode(A,B,Q,R,[],PT,tspan) solves the Riccati differential equation for , given the state matrix , input matrix , state weighting matrix , input weighting matrix , terminal condition , and the time span tspan over which to solve. tspan can be specified either as the 1×2 double [t0,T] where is the initial time and is the final time, or as a 1×(N+1) vector of times [t0,t1,...,tNminus1,T] at which to return the solution for . It is assumed that the cross-coupling weighting matrix is .

[t,P] = solve_riccati_ode(A,B,Q,R,S,PT,tspan) does the same as the syntax above, but this time the cross-coupling weighting matrix is specified.

The time vector, , is defined as

The ith "layer" of P (i.e. P(:,:,i)) stores , where is the time stored in the ith element of the time vector, .

• See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.
• See Riccati_Differential_Equation.pdf (also included with download) for additional documentation.