System for Continuous-Time Optimization with Pre-Defined Finite-Time Convergence

Patent metadata

Field	Value
Publication number	US-2021124320-A1
Application number	US-201916665670-A
Country	US
Kind code	A1
Filing date	Oct 28, 2019
Priority date	Oct 28, 2019
Publication date	Apr 29, 2021
Grant date	—

Abstract

A controller for controlling a system is provided. The controller performs measuring variables via an interface to generate a vector of variables, providing a cost function, with respect to the system, based on the vector variables using weighting factors, wherein the vector variables are represented by a time-step, computing first-derivative of the cost function at an initial time-step, obtaining a convergence time from the first-derivative of the cost function, computing second derivative of the cost function and generating an optimization differential equation based on the first and second derivatives of the cost function, proceeding, starting with the initial time-step, to obtain a value of the optimization differential equation by solving the optimization differential equation, in an iteration manner, with a predetermined time step being multiplied with the value of the solved differential equation to obtain next vector variables corresponding to a next iteration time-step, until the time-step reaches the convergence time, and outputting optimal values of the vector of variables and the cost function.

First claim

We claim:

1 . A controller for controlling a system comprising:
an interface configured to receive measurement signals from sensor units and output control signals to the system to be controlled; a memory to store computer-executable algorithms including variable measuring algorithm, cost function equations, ordinary differential equation (ODE) and ordinary differential inclusion (ODI) solving algorithms and Optimal variables' values output algorithm; a processor, in connection with the memory, configured to perform steps of receiving measuring variables via the interface to generate a vector of variables; providing a cost function equation, with respect to the system, based on the vector variables using weighting factors, wherein the vector variables are represented by a time-step; computing first-derivative of the cost function at an initial time-step;
obtaining a convergence time from the first-derivative of the cost function;
computing second derivative of the cost function and generating an optimization differential equation based on the first and second derivatives of the cost function;
proceeding, starting with the initial time-step, to obtain a value of the optimization differential equation or differential inclusion by solving the optimization differential equation or the differential inclusion, in an iteration manner, with a predetermined time step being multiplied with the value of the solved differential equation to obtain next vector variables corresponding to a next iteration time-step, until the time-step reaches the convergence time; and
outputting optimal values of the vector of variables and the cost function.

2 . The controller of claim 1 , wherein the optimization differential equation is solved by a first order Euler steps:
x ( k+ 1)= x ( k )+ h.F ( k,x ( k )),
where h>0 is the discretization time-step, and k=0, 1, 2, . . . , is the discretization index, here, F is the optimization differential equation or differential inclusion.

3 . The controller of claim 1 , wherein the optimization differential equation is solved by the Runge-Kutta discretization steps.

4 . The controller of claim 1 , wherein the optimization differential equation is solved by a disctization steps:

5 . The controller of claim 1 , wherein the optimization differential equation is

x
.

=

-
c

⁢



∇

⁢

f
⁡

(
x
)



p

⁢

[

∇

2

⁢

f
⁡

(
x
)

]

r

⁢

∇

⁢

f
⁡

(
x
)

∇

⁢

f
⁡

(
x
)

T

[

∇

2

⁢

f
⁡

(
x
)

]

r
+
1

⁢

∇

⁢

f
⁡

(
x
)

,

where the constant coefficient c,p,r, are such that c>0, p∈[1,2), and r∈R, and ƒ represents the cost function, ∇ƒ(x) represents the gradient of the cost function, and ∇ 2 ƒ(x) the Hessian of the cost function.

6 . The controller of claim 1 , wherein the optimization differential equation is

x
.

=

-
c

⁢



∇

⁢

f
⁡

(
x
)



1

p
-
1

⁢

[

∇

Assignees

• Mitsubishi Electric Res Laboratories Inc

Inventors

• Benosman Mouhacine
• Romero Orlando

Classifications

• G05B13/041

  in which a variable is automatically adjusted to optimise the performance · CPC title

• G06F17/13 Primary

  Differential equations (using digital differential analysers G06F7/64) · CPC title

• G05B17/02 Primary

  electric · CPC title

• F24F11/62

  characterised by the type of control or by internal processing, e.g. using fuzzy logic, adaptive control or estimation of values · CPC title

• G05B2219/2614

  HVAC, heating, ventillation, climate control · CPC title