Adaptive model predictive control discrete systems with unknown input

The model of the object, observations and output is described by the following linear difference equations: ^xt+1 = ^A(⁰t)^xt + ^B(⁰t^)ut +^Ir, + ^w,^, xt|t=0 = ^x0 ^, Yt = ^Hx, + ^v,^, yt = ^Gx,^, where x_t e Rⁿ is the state of the object, u_t e R^m is the control (known input), y_t e R^l is the observations vector, r_t e R^q is an unknown input, y_t e R^p is the controlled output, 9_t is an unknown parameter vector, A(9_t) , B(9_t) , I, H, G are matrices. The random perturbations wt, the measurement noise vt, and the vector of initial conditions x0 are not correlated to each other and obey a Gaussian distribution with characteristics: M{w_t} = 0, M{v } = 0, M{wwT} = W8_t,k, M{vvT} = Vb_tJc, M{w_tvl} = 0, M{x₀} = x , M{(x₀ -x₀)(x₀ -x₀)^T} = p. . Restrictions on the state and control vectors are representable in the form a (t) < S₁ x_t < a₂ (t), ф₁ (x_t, t) < S₂u_t < ф₂ (x_t, t), where S1 and S2 are structure matrices of full rank consisting of zeros and ones defining the components of the vectors xt and ut, on which constraints are imposed; a₁(t), a₂(t), ф₁(x_t, t) , ф₂(x_t, t) are the given vectors and vector-functions. Based on the minimization of the criterion 1 ^N 2 1 ^M 2 ^J Cw ^,Ut⁾=2 E||^yt+kit^- yt+k||_C + - S||^ut+kit^- ut+k-1it||_B ² k =1 ² k=1 algorithms for the synthesis of adaptive predictive control of a discrete object under conditions of incomplete information about the parameters of the model and in the presence of an unknown input in the model of the object are considered. The application of the algorithm of adaptive predictive control to the economic system of production, storage and delivery of goods to consumers is given.

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