Partial-form model-free adaptive disturbance compensation control in the presence of measurable disturbances

A method of partial-form model-free adaptive disturbance compensation control in the presence of measurable disturbances, executed on a hardware platform for controlling a controlled plant subject to measurable disturbances, said controlled plant being a multi-input multi-output (MIMO) system with a predetermined number of control inputs and a predetermined number of system outputs, said method comprising:

• obtaining measurable disturbances at time k, establishing a dynamic data model of said controlled plant subject to measurable disturbances, wherein said dynamic data model is described by a pseudo Jacobian input matrix θ(k) and a pseudo Jacobian disturbance matrix χ(k);
• constructing cost functions and solving optimization problems for said cost functions to find an optimal value of said pseudo Jacobian input matrix θ(k) and an optimal value of said pseudo Jacobian disturbance matrix χ(k);
• utilizing said measurable disturbances at time k, employing said dynamic data model described by said optimal value of said pseudo Jacobian input matrix θ(k) and said optimal value of said pseudo Jacobian disturbance matrix χ(k), designing a partial-form model-free adaptive disturbance compensation control law in the presence of measurable disturbances as:
• u
• ⁡
• (
• k
• )
• =
• u
• ⁡
• (
• k
• -
• 1
• )
• +
• π
• p
• (
• k
• )
• ⁢
• Δ
• ⁢
• E
• ⁡
• (
• k
• )
• +
• ω
• p
• (
• k
• )
• ⁢
• Δ
• ⁢
• D
• ⁡
• (
• k
• )
• where k is a positive integer;
• u(k) is a control input vector of said controlled plant at time k;
• ΔE(k)=[−e(k)T, Δe(k)T, . . . , Δe(k−L+2)T]T, ΔD(k)=[Δd(k)T, . . . , Δd(k−L+1)T]T;
• e(k) is a system error vector of said controlled plant at time k, e(k)=[e1(k), . . . , en(k)]T, Δe(k)=e(k)−e(k−1);
• e(k)=y*(k)−y(k), y*(k) is a desired system output vector of said controlled plant at time k,
• y
• *
• (
• k
• )
• =
• [
• y
• 1
• *
• (
• k
• )
• ,
• …
• ,
• y
• n
• *
• (
• k
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• ]
• T
• ;
• n is a total number of system outputs in said controlled plant, n is a positive integer greater than 1;
• d(k) is a measurable disturbance vector in said controlled plant at time k, Δd(k)=d(k)−d(k−1);
• L is linearized length constant and is positive integer;
• πp(k) is a partial-form adaptive input matrix at time k and ωp(k) is a partial-form adaptive disturbance matrix at time k;
• constructing an energy function and solving said energy function by using a momentum gradient descent method to find an optimal value of said partial-form adaptive input matrix πp(k) and an optimal value of said partial-form adaptive disturbance matrix ωp(k);
• controlling said controlled plant by using said partial-form model-free adaptive disturbance compensation control law in the presence of measurable disturbances with said optimal value of partial-form adaptive input matrix πp(k) and said optimal value of partial-form adaptive disturbance matrix ωp(k);
• and
• generating an actual system output vector of said controlled plant based on the application of said control law.