Optimizer#
- class Optimizer[source]#
Bases:
object
The base clase for the optimization based state estimation (MHE) and predictive controller (MPC). This class establishes the jointly used attributes, methods and properties.
Warning
The
Optimizer
base class can not be used independently. The methods and properties are inherited todo_mpc.estimator.MHE
anddo_mpc.controller.MPC
.
Methods#
compile_nlp#
- compile_nlp(self, overwrite=False, cname='nlp.c', libname='nlp.so', compiler_command=None)#
Compile the NLP. This may accelerate the optimization. As compilation is time consuming, the default option is to NOT overwrite (
overwrite=False
) an existing compilation. If an existing compilation with the namelibname
is found, it is used. This can be dangerous, if the NLP has changed (user tweaked the cost function, the model etc.).Warning
This feature is experimental and currently only supported on Linux and MacOS.
What happens here?
The NLP is written to a C-file (
cname
)The C-File (
cname
) is compiled. The custom compiler uses:
gcc -fPIC -shared -O1 {cname} -o {libname}
The compiled library is linked to the NLP. This overwrites the original NLP. Options from the previous NLP (e.g. linear solver) are kept.
self.S = nlpsol('solver_compiled', 'ipopt', f'{libname}', self.nlpsol_opts)
- Parameters:
overwrite (
bool
) – If True, the existing compiled NLP will be overwritten.cname (
str
) – Name of the C file that will be exported.libname (
str
) – Name of the shared library that will be created after compilation.compiler_command (
str
) – Command to use for compiling. If None, the default compiler command will be used. Please make sure to use matching strings forlibname
when supplying your custom compiler command.
- Return type:
None
create_nlp#
- create_nlp(self)#
Create the optimization problem. Typically, this method is called internally from
setup()
.Users should only call this method if they intend to modify the objective with
nlp_obj
, the constraints withnlp_cons
,nlp_cons_lb
andnlp_cons_ub
.To finish the setup process, users MUST call
create_nlp()
afterwards.Note
Do NOT call
setup()
if you intend to go the manual route withprepare_nlp()
andcreate_nlp()
.Note
Only AFTER calling
prepare_nlp()
the previously mentionned attributesnlp_obj
,nlp_cons
,nlp_cons_lb
,nlp_cons_ub
become available.- Returns:
None
– None
get_tvp_template#
- get_tvp_template(self)#
Obtain output template for
set_tvp_fun()
.The method returns a structured object with
n_horizon+1
elements, and a set of time-varying parameters (as defined indo_mpc.model.Model
) for each of these instances. The structure is initialized with all zeros. Use this object to define values of the time-varying parameters.This structure (with numerical values) should be used as the output of the
tvp_fun
function which is set to the class withset_tvp_fun()
. Use the combination ofget_tvp_template()
andset_tvp_fun()
.Example:
# in model definition: alpha = model.set_variable(var_type='_tvp', var_name='alpha') beta = model.set_variable(var_type='_tvp', var_name='beta') ... # in optimizer configuration: tvp_temp_1 = optimizer.get_tvp_template() tvp_temp_1['_tvp', :] = np.array([1,1]) tvp_temp_2 = optimizer.get_tvp_template() tvp_temp_2['_tvp', :] = np.array([0,0]) def tvp_fun(t_now): if t_now<10: return tvp_temp_1 else: tvp_temp_2 optimizer.set_tvp_fun(tvp_fun)
- Returns:
Union
[SXStruct
,MXStruct
] – Casadi SX or MX structure
prepare_nlp#
- prepare_nlp(self)#
Prepare the optimization problem. Typically, this method is called internally from
setup()
.Users should only call this method if they intend to modify the objective with
nlp_obj
, the constraints withnlp_cons
,nlp_cons_lb
andnlp_cons_ub
.To finish the setup process, users MUST call
create_nlp()
afterwards.Note
Do NOT call
setup()
if you intend to go the manual route withprepare_nlp()
andcreate_nlp()
.Note
Only AFTER calling
prepare_nlp()
the previously mentionned attributesnlp_obj
,nlp_cons
,nlp_cons_lb
,nlp_cons_ub
become available.- Returns:
None
– None
reset_history#
- reset_history(self)#
Reset the history of the optimizer. All data from the
do_mpc.data.Data
instance is removed.- Return type:
None
set_nl_cons#
- set_nl_cons(self, expr_name, expr, ub=inf, soft_constraint=False, penalty_term_cons=1, maximum_violation=inf)#
Introduce new constraint to the class. Further constraints are optional. Expressions must be formulated with respect to
_x
,_u
,_z
,_tvp
,_p
. They are implemented as:\[m(x,u,z,p_{\text{tv}}, p) \leq m_{\text{ub}}\]Setting the flag
soft_constraint=True
will introduce slack variables \(\epsilon\), such that:\[\begin{split}m(x,u,z,p_{\text{tv}}, p)-\epsilon &\leq m_{\text{ub}},\\ 0 &\leq \epsilon \leq \epsilon_{\text{max}},\end{split}\]Slack variables are added to the cost function and multiplied with the supplied penalty term. This formulation makes constraints soft, meaning that a certain violation is tolerated and does not lead to infeasibility. Typically, high values for the penalty are suggested to avoid significant violation of the constraints.
- Parameters:
expr_name (
str
) – Arbitrary name for the given expression. Names are used for key word indexing.expr (
Union
[SX
,MX
]) – CasADi SX or MX function depending on_x
,_u
,_z
,_tvp
,_p
.ub (
float
) – Upper boundsoft_constraint (
bool
) – Flag to enable soft constraintpenalty_term_cons (
int
) – Penalty term constantmaximum_violation (
float
) – Maximum violation
- Raises:
assertion – expr_name must be str
assertion – expr must be a casadi SX or MX type
- Returns:
Union
[SX
,MX
] – Returns the newly created expression. Expression can be used e.g. for the RHS.
set_tvp_fun#
- set_tvp_fun(self, tvp_fun)#
Set function which returns time-varying parameters.
The
tvp_fun
is called at each optimization step to get the current prediction of the time-varying parameters. The supplied function must be callable with the current time as the only input. Furthermore, the function must return a CasADi structured object which is based on the horizon and on the model definition. The structure can be obtained withget_tvp_template()
.Example:
# in model definition: alpha = model.set_variable(var_type='_tvp', var_name='alpha') beta = model.set_variable(var_type='_tvp', var_name='beta') ... # in optimizer configuration: tvp_temp_1 = optimizer.get_tvp_template() tvp_temp_1['_tvp', :] = np.array([1,1]) tvp_temp_2 = optimizer.get_tvp_template() tvp_temp_2['_tvp', :] = np.array([0,0]) def tvp_fun(t_now): if t_now<10: return tvp_temp_1 else: tvp_temp_2 optimizer.set_tvp_fun(tvp_fun)
Note
The method
set_tvp_fun()
. must be called prior to setup IF time-varying parameters are defined in the model. It is not required to call the method if no time-varying parameters are defined.- Parameters:
tvp_fun (
Callable
[[float
],Union
[SXStruct
,MXStruct
]]) – Function that returns the predicted tvp values at each timestep. Must have single input (float) and return astructure3.DMStruct
(obtained withget_tvp_template()
).- Return type:
None
solve#
- solve(self)#
Solves the optmization problem.
The current problem is defined by the parameters in the
opt_p_num
CasADi structured Data.Typically,
opt_p_num
is prepared for the current iteration in themake_step()
method. It is, however, valid and possible to directly set paramters inopt_p_num
before callingsolve()
.The method updates the
opt_p_num
andopt_x_num
attributes of the class. By resettingopt_x_num
to the current solution, the method implicitly enables warmstarting the optimizer for the next iteration, since this vector is always used as the initial guess. :rtype:None
Warning
The method is part of the public API but it is generally not advised to use it. Instead we recommend to call
make_step()
at each iterations, which acts as a wrapper forsolve()
.- Raises:
asssertion – Optimizer was not setup yet.
Attributes#
bounds#
- Optimizer.bounds#
Query and set bounds of the optimization variables. The
bounds()
method is an indexed property, meaning getting and setting this property requires an index and calls this function. The power index (elements are separated by commas) must contain atleast the following elements:order
index name
valid options
1
bound type
lower
andupper
2
variable type
_x
,_u
and_z
(and_p_est
for MHE)3
variable name
Names defined in
do_mpc.model.Model
.Further indices are possible (but not neccessary) when the referenced variable is a vector or matrix.
Example:
# Set with: optimizer.bounds['lower','_x', 'phi_1'] = -2*np.pi optimizer.bounds['upper','_x', 'phi_1'] = 2*np.pi # Query with: optimizer.bounds['lower','_x', 'phi_1']
lb_opt_x#
- Optimizer.lb_opt_x#
Query and modify the lower bounds of all optimization variables
opt_x
. This is a more advanced method of setting bounds on optimization variables of the MPC/MHE problem. Users with less experience are advised to usebounds
instead.The attribute returns a nested structure that can be indexed using powerindexing. Please refer to
opt_x
for more details.Note
The attribute automatically considers the scaling variables when setting the bounds. See
scaling
for more details.Note
Modifications must be done after calling
prepare_nlp()
orsetup()
respectively.
nlp_cons#
- Optimizer.nlp_cons#
Query and modify (symbolically) the NLP constraints. Use the variables in
opt_x
andopt_p
.Prior to calling
create_nlp()
this attribute returns a list of symbolic constraints. After callingcreate_nlp()
this attribute returns the concatenation of this list and the attribute cannot be altered anymore.It is advised to append to the current list of
nlp_cons
:mpc.prepare_nlp() # Create new constraint: Input at timestep 0 and 1 must be identical. extra_cons = mpc.opt_x['_u', 0, 0]-mpc.opt_x['_u',1, 0] mpc.nlp_cons.append( extra_cons ) # Create appropriate upper and lower bound (here they are both 0 to create an equality constraint) mpc.nlp_cons_lb.append(np.zeros(extra_cons.shape)) mpc.nlp_cons_ub.append(np.zeros(extra_cons.shape)) mpc.create_nlp()
See the documentation of
opt_x
andopt_p
on how to query these attributes.Warning
This is a VERY low level feature and should be used with extreme caution. It is easy to break the code.
Be especially careful NOT to accidentially overwrite the default objective.
Note
Modifications must be done after calling
prepare_nlp()
and before callingcreate_nlp()
nlp_cons_lb#
- Optimizer.nlp_cons_lb#
Query and modify the lower bounds of the
nlp_cons
.Prior to calling
create_nlp()
this attribute returns a list of lower bounds matching the list of constraints obtained withnlp_cons
. After callingcreate_nlp()
this attribute returns the concatenation of this list.Values for lower (and upper) bounds MUST be added when adding new constraints to
nlp_cons
.Warning
This is a VERY low level feature and should be used with extreme caution. It is easy to break the code.
Note
Modifications must be done after calling
prepare_nlp()
nlp_cons_ub#
- Optimizer.nlp_cons_ub#
Query and modify the upper bounds of the
nlp_cons
.Prior to calling
create_nlp()
this attribute returns a list of upper bounds matching the list of constraints obtained withnlp_cons
. After callingcreate_nlp()
this attribute returns the concatenation of this list.Values for upper (and lower) bounds MUST be added when adding new constraints to
nlp_cons
.Warning
This is a VERY low level feature and should be used with extreme caution. It is easy to break the code.
Note
Modifications must be done after calling
prepare_nlp()
nlp_obj#
- Optimizer.nlp_obj#
Query and modify (symbolically) the NLP objective function. Use the variables in
opt_x
andopt_p
.It is advised to add to the current objective, e.g.:
mpc.prepare_nlp() # Modify the objective mpc.nlp_obj += sum1(vertcat(*mpc.opt_x['_x', -1, 0])**2) # Finish creating the NLP mpc.create_nlp()
See the documentation of
opt_x
andopt_p
on how to query these attributes.Warning
This is a VERY low level feature and should be used with extreme caution. It is easy to break the code.
Be especially careful NOT to accidentially overwrite the default objective.
Note
Modifications must be done after calling
prepare_nlp()
and before callingcreate_nlp()
scaling#
- Optimizer.scaling#
Query and set scaling of the optimization variables. The
Optimizer.scaling()
method is an indexed property, meaning getting and setting this property requires an index and calls this function. The power index (elements are seperated by comas) must contain atleast the following elements:order
index name
valid options
1
variable type
_x
,_u
and_z
(and_p_est
for MHE)2
variable name
Names defined in
do_mpc.model.Model
.Further indices are possible (but not neccessary) when the referenced variable is a vector or matrix.
Example:
# Set with: optimizer.scaling['_x', 'phi_1'] = 2 optimizer.scaling['_x', 'phi_2'] = 2 # Query with: optimizer.scaling['_x', 'phi_1']
Scaling factors \(a\) affect the MHE / MPC optimization problem. The optimization variables are scaled variables:
\[\bar\phi = \frac{\phi}{a_{\phi}} \quad \forall \phi \in [x, u, z, p_{\text{est}}]\]Scaled variables are used to formulate the bounds \(\bar\phi_{lb} \leq \bar\phi_{ub}\) and for the evaluation of the ODE. For the objective function and the nonlinear constraints the unscaled variables are used. The algebraic equations are also not scaled.
Note
Scaling the optimization problem is suggested when states and / or inputs take on values which differ by orders of magnitude.
ub_opt_x#
- Optimizer.ub_opt_x#
Query and modify the lower bounds of all optimization variables
opt_x
. This is a more advanced method of setting bounds on optimization variables of the MPC/MHE problem. Users with less experience are advised to usebounds
instead.The attribute returns a nested structure that can be indexed using powerindexing. Please refer to
opt_x
for more details.Note
The attribute automatically considers the scaling variables when setting the bounds. See
scaling
for more details.Note
Modifications must be done after calling
prepare_nlp()
orsetup()
respectively.