Interfaces

Classes

Class name	Description
OptimalControlProblem	Create an OCP
NMPCSolver	Configurate the solver
OCPSolver	Solve the very first OCP
DynamicSystem	Create a dynamic system

OptimalControlProblem

Formulate an OCP.

Example

./NMPC_Problem_Formulation.m

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

Functions	Description
OptimalControlProblem	Constructor. Input: muDim: [1,1], dimension of mu. uDim: [1,1], dimension of u. xDim: [1,1], dimension of x. pDim: [1,1], dimension of p. T: [1,1], prediction horizon. N: [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, function L. Output: none.
setC	Set C. Input: C: symbolic expression, 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.
setDiscretizationMethod	Set the discretization method. Input: method: string, 'Euler' 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', method of Hessian approximation. Output: none
codeGen	Generate necessary files. Input: none. Output: none.

OCPSolver

Solve the very first OCP offline.

Example

./NMPC_Problem_Formulation.m

Properties	Description
OCP	OptimalControlProblem, OptimalControlProblem object.
NMPCSolver	NMPCSolver, NMPCSolver object.
x0	[xDim,1], initial state.
lambda	[xDim,N], multipliers.
mu	[muDim,N], multipliers.
u	[uDim,N], inputs.
x	[xDim,N], states.
p	[pDim,N], given parameters.
LAMBDA	[xDim,xDim,N], dependent variable LAMBDA.

Functions	Description
OCPSolver	Constructor. Input: OCP: OptimalControlProblem, OptimalControlProblem object. NMPCSolver: NMPCSolver, NMPCSolver object. x0: [xDim,1], initial state. pVal: [pDim,N], given parameters. Output: OCPSolver
OCPSolve	Solve the OCP with a providing initial guess offline. Input: lambdaInitGuess: [xDim,N], initial guess of lambda. muInitGuess: [muDim,N], initial guess of mu. uInitGuess: [uDim,N], initial guess of u. xInitGuess: [xDim,N], initial guess of x. method: string, 'fsolve' or 'NMPC_Iter_GaussNewton', solver. Output: lambda: [xDim,N], optimal value of lambda. mu: [muDim,N], optimal value of mu. u: [uDim,N], optimal value of u. x: [xDim,N], optimal value of x.
initFromMatFile	Initialize from file with automatic interpolation. Input: matFile: string, file name of the mat file. Output: lambda: [xDim,N], interpolated value of lambda. mu: [muDim,N], interpolated value of mu. u: [uDim,N], interpolated value of u. x: [xDim,N], interpolated value of x.
initFromStartEnd	Initialize from the start and the end values by linear interpolation. Input: lambdaStart: [xDim,1], start value of lambda. muStart: [muDim,1], start value of mu. uStart: [uDim,1], start value of u. xStart: [xDim,1], start value of x. lambdaEnd: [xDim,1], end value of lambda. muEnd: [muDim,1], end value of mu. uEnd: [uDim,1], end value of u. xEnd: [xDim,1], end value of x. method: string, 'fsolve' or 'NMPC_Iter_GaussNewton', solver. Output: lambda: [xDim,N], interpolated value of lambda. mu: [muDim,N], interpolated value of mu. u: [uDim,N], interpolated value of u. x: [xDim,N], interpolated value of x.
getLAMBDA	Get the dependent variable LAMBDA from the given x0, lambda, mu, u, x, p. Input: x0: [xDim,1], initial state. lambda: [xDim,N], lambda. mu: [muDim,N], mu. u: [uDim,N], u. x: [xDim,N], x. p: [pDim,N], p. Output: LAMBDA: [xDim,xDim,N]
getCost	Get the cost function from the given u, x, p. Input: u: [uDim,N], u. x: [xDim,N], x. p: [pDim,N], p. Output: cost: [1,1]

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, input vector.
x	symbolic vector, state vector.
p	symbolic vector, parameter vector.
f	symbolic expression, function f.
M	symbolic expression, matrix M .
isMEnabled	bool, whether the M matrix is enabled.

Functions	Description
DynamicSystem	Constructor. Input: uDim: [1,1], dimension of u. xDim: [1,1], dimension of x. pDim: [1,1], dimension of p. Output: DynamicSystem
setf	Set f. Input: f: symbolic expression, function f. Output: none.
setM	Set M. Input: M: symbolic expression, 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_Iter	Perform one iteration for solving the KKT conditions.
NMPC_Iter_CodeGen	Generate code for function NMPC_Iter.
SIM_Plant_RK4	Simulate the dynamic system using the 4-order Runge-Kutta method.
Timer	Specify your own timer function.

NMPC_Iter

Example

./Simu_Matlab.m

Function name	NMPC_Iter
Description	Perform one iteration to solve the KKT conditions.
Input	x0: [xDim,1], initial state. lambda: [xDim,N/DoP,DoP]. mu: [muDim,N/DoP,DoP]. u: [uDim,N/DoP,DoP]. x: [xDim,N/DoP,DoP]. p: [pDim,N/DoP,DoP], given parameters. LAMBDA: [xDim,xDim,N/DoP,DoP]. discretizationMethod: string, 'Euler' or 'RK4'. isMEnabled: bool.
Output	lambda: [xDim,N/DoP,DoP]. mu: [muDim,N/DoP,DoP]. u: [uDim,N/DoP,DoP]. x: [xDim,N/DoP,DoP]. LAMBDA: [xDim,xDim,N/DoP,DoP]. cost: [1,1], evaluation of the cost function after iteration. error: [1,1], Euclidean norm of the KKT conditions. timeElapsed: [1,1], computation time.

NMPC_Iter_CodeGen

Example

./Simu_Simulink_Setup.m

Function name	NMPC_Iter_CodeGen
Description	Generate code for function NMPC_Iter.
Input	target: string, 'mex', 'dll', or 'mex'. targetLang: string, 'C' or 'C++'. args: cell, arguments applied to NMPC_Iter.
Output	None

SIM_Plant_RK4

Example

./Simu_Matlab.m

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