Interfaces

Classes

Class name	Description
OptimalControlProblem	Formulate an OCP
NMPCSolver	Configurate the NMPC solver
DynamicSystem	Construct a dynamic system

OptimalControlProblem

Formulate an OCP.

Example

./NMPC_Problem_Formulation.m

Properties	Description
dim	structure.{lambda,mu,u,x,z,p}, dimensions of lambda, mu, u, x, z, p.
lambda	symbolic vector [dim.x,1], multiplier vector.
mu	symbolic vector [dim.mu,1], multiplier vector.
u	symbolic vector [dim.u,1], input vector.
x	symbolic vector [dim.x,1], state vector.
z	symbolic vector [zDim,1], multiplier vector.
p	symbolic vector [pDim,1], parameter vector.
f	symbolic expression [dim.x,1], function f.
M	symbolic expression [dim.x,dim.x], matrix M .
L	symbolic expression [1,1], function L.
C	symbolic expression [dim.mu,1], function C.
G	symbolic expression [dim.z,1], function G.
N	positive integer [1,1], number of discretization grids N.
T	positive [1,1], prediction horizon T.
deltaTau	positive [1,1], discretization size (T/N).
discretizationMethod	string, discretization method.
isMEnabled	bool, whether the M matrix is enabled.

Functions	Description
OptimalControlProblem	Constructor. Input: dim.u: positive integer [1,1], dimension of u. dim.x: positive integer [1,1], dimension of x. pDim: nonnegtive integer [1,1], dimension of p. N: positive integer [1,1], number of discretization grids. Output: OptimalControlProblem
setf	Set f. Inherit from DynamicSystem
setM	Set M. Inherit from DynamicSystem
setStateName	Give names to all or part of the states. Inherit from DynamicSystem
setInputName	Give names to all or part of the inputs. Inherit from DynamicSystem
setParameterName	Give names to all or part of the parameters. Inherit from DynamicSystem
setL	Set L. Input: L: symbolic expression [1,1], function L. Output: none.
setC	Set C. Input: C: symbolic expression [dim.mu,1], function C. Output: none.
setT	Set T. Input: T: symbolic variable/double [1,1], must be included in p if it is a symbolic variable. Output: none.
setG	Set G. Input: C: symbolic expression [dim.z,1], function G. Output: none.
setDiscretizationMethod	Set the discretization method. Input: method: string, 'Euler', 'RK2', or 'RK4', discretization method. Output: none
codeGen	Generate necessary files. Input: none. Output: none.

NMPCSolver

Configurate the NMPC solver.

Example

./NMPC_Problem_Formulation.m

Properties	Description
OCP	OptimalControlProblem, OptimalControlProblem object.
HessianApproximation	string, Hessian approximation method.

Functions	Description
NMPCSolver	Constructor. Input: OCP: OptimalControlProblem, OptimalControlProblem object. Output: NMPCSolver
setHessianApproximation	Set the Hessian approximation method. Input: method: string, 'Newton', 'GaussNewton', or 'GaussNewtonLC', Hessian approximation method. Output: none
codeGen	Generate necessary files. Input: none. Output: none.

DynamicSystem

Construct a dynamic system $M(u(t),x(t),p(t))\dot{x}=f(u(t),x(t),p(t))$.

Example

./NMPC_Problem_Formulation.m

Properties	Description
dim	structure.{u;x;p}, dimensions of u, x, p.
u	symbolic vector [dim.u,1], input vector.
x	symbolic vector [dim.x,1], state vector.
p	symbolic vector [pDim,1], parameter vector.
f	symbolic expression [dim.x,1], function f.
M	symbolic expression [dim.x,dim.x], matrix M .
isMEnabled	bool, whether the M matrix is enabled.

Functions	Description
DynamicSystem	Constructor. Input: dim.u: [1,1], dimension of u. dim.x: [1,1], dimension of x. pDim: [1,1], dimension of p. Output: DynamicSystem
setf	Set f. Input: f: symbolic expression [dim.x,1], function f. Output: none.
setM	Set M. Input: M: symbolic expression [dim.x,dim.x], M matrix. Output: none.
setStateName	Give names to all or part of the states. Example: [X,Y,Z] =~.setStateName({'X','Y','Z'}); [X,Z] =~.setStateName({'X','Z'},[1 3]);
setInputName	Give names to all or part of the inputs. Example: [F1,F2,F3] =~.setInputName({'F1','F2','F3'}; [F1,F3] =~.setInputName({'F1','F3'},[1 3]);
setParameterName	Give names to all or part of the parameters. Example: [a,b,c] =~.setParameterName({'a','b','c'}; [a,c] =~.setParameterName({'a','c'},[1 3]);
codeGen	Generate necessary files. Input: none. Output: none.

Functions

Function name	Description
NMPC_Solve	Solve the NMPC problem.
createOptions	Create an option struct for NMPC_Solve.
NMPC_Solve_CodeGen	Generate code for NMPC_Solve.
SIM_Plant_RK4	Simulate the dynamic system using the 4-th order Runge-Kutta method.
Timer	Measure the current time.

NMPC_Solve

Example

./Simu_Matlab.m

Function name	NMPC_Solve
Description	Solve the NMPC problem.
Input	x0: [dim.x,1], initial state. p: [pDim,N], given parameters. options: struct, options.
Output	solution: struct, solution. output: struct, output information.

createOptions

Example

./Simu_Matlab.m

Function name	createOptions
Description	Create an option struct for NMPC_Solve.
Input	None
Output	options: struct, options.

NMPC_Solve_CodeGen

Example

./Simu_Simulink_Setup.m

Function name	NMPC_Solve_CodeGen
Description	Generate code for function NMPC_Solve.
Input	target: string, 'mex', 'dll', or 'mex', target. targetLang: string, 'C' or 'C++', target language. options: struct, options.
Output	None

SIM_Plant_RK4

Example

./Simu_Matlab.m

Function name	SIM_Plant_RK4
Description	Simulate the dynamic system using the 4-th order Runge-Kutta method.
Input	u: [dim.u,1], inputs applied to the plant. x: [dim.x,1], current state of the plant. p: [pDim,1], given parameters. Ts: positive [1,1], sampling interval.
Output	xNext: [dim.x,1], next state of the plant.

Timer

Example

./Timer.m

Function name	Timer
Description	Measure the current time.
Input	None
Output	t: [1,1], current time.
Statement	Create Timer.m in the working directory to specify your own timer function.